Description : What is the point of contact when the line y equals 2x meets the circle x2 plus y2 -8x -y plus 5 equals 0?
Last Answer : If: y = 2xThen: y^2 = 4x^2If: x^2 +y^2 -8x -y +5 = 0Then: x^2 +4x^2 -8x -2x +5 = 0Transposing terms: 5x^2 -10x +5 = 0Dividing all terms by 5: x^2 -2x +1 = 0Factorizing the above: (x-1)(x-1) = 0 meaning x = 1By substitution into original equations point of contact is madeat: (1, 2)
Description : What is the distance from a point on the x axis to the centre of a circle when a tangent line at the point 3 4 meets the circle of x2 plus y2 -2x -6y plus 5 equals 0?
Last Answer : Circle equation: x^2 +y^2 -2x -6y +5 = 0Completing the squares: (x-1)^2 +(y-3)^2 = 5Centre of circle: (1, 3)Tangent line meets the x-axis at: (0, 5)Distance from (0, 5) to (1, 3) = 5 units using the distanceformula
Description : What is the point of contact between the line y equals x plus 4 and the circle x2 plus y2 -8x plus 4y equals 30?
Last Answer : Equations: y = x+4 and x^2 +y^2 -8x +4y = 30It appears that the given line is a tangent line to the givencircle and the point of contact works out as (-1, 3)
Description : If z equals yf x2 - y2 show that ydz divided by dx plus xdz divided by dy equals xz divided by y?
Last Answer : 4
Description : What is the length of a tangent line from the point 7 -2 to a point when it touches the circle x2 plus y2 -10 equals 49?
Last Answer : x² + y² - 10 = 49→ x² + y² = 59= (x - 0)² + (y - 0)² = (√59)²→ circle has centre (0, 0) - the origin - and radius √59The point (7, -2) has a distance from the centre of the circleof:√((7 - 0)² + (-2 - 0)²) = √(7² + (-2)²) = √(49 + 4) = √53
Description : What is the length of the circle radius if the circle is x2 plus y2 equals 1?
Last Answer : The center of the circle is at (0, 0) and its radius is thesquare root of 1 which is 1
Description : What is the length of the tangent line from the point 9 0 to the circle x2 plus 8x plus y2 -9 equals 0?
Last Answer : Equation of circle: x^2 +8x +y^2 -9 = 0Completing the square: (x+4)^2 +y^2 = 25Radius of circle: 5Center of circle: (-4, 0)Distance from (9, 0) to (-4, 0) = 13 which is ... the length of the tangent line is 12 unitsNote that the tangent line of a circle meets the radius of thecircle at right angles
Description : What is the equation of the tangent line that meets the circle x2 -4x plus y2 -6y equals 4 at the point 6 4?
Last Answer : Circle equation: x^2 -4x +y^2 -6y = 4Completing the squares: (x-2)^2 +(y-3)^2 = 17Point of contact: (6, 4)Center of circle: (2, 3)Slope of radius: 1/4Slope of tangent line: -4Tangent equation: y-4 = -4(x-6) => y = -4x+28Tangent line equation in its general form: 4x+y-28 = 0
Description : What is the length of the tangent line from the point 8 2 to a point where it meets the circle x2 plus y2 -4x -8y -5 equals 0?
Last Answer : Equation of circle: x^2 +y^2 -4x -8y -5 = 0Completing the squares: (x-2)^2 +(y-4)^2 = 25 which is radiussquaredCenter of circle: (2, 4)Tangent line originates from: (8, ... angle triangleUsing Pythagoras theorem: distance^2 minus radius^2 = 15Therefore length of tangent line is the square root of 15
Description : What is the center and the radius of the circle x2 plus y2 -4x -6y -3 equals 0?
Last Answer : Equation of circle: x^2 +y^2 -4x -6y -3 = 0Completing the squares: (x-2)^2 +(y-3)^2 = 16 square unitsTherefore center of circle is at (2, 3) and its radius is 4units
Description : What is the center and the radius of the circle x2 plus y2 equals 12x -10y -12?
Last Answer : Equation of circle: x^2 +y^2 = 12x-10y-12Completing the squares: (x-6)^2 +(y+5)^2 = 49So center of circle is at (6, -5) and its radius is 7 units
Description : How many real solutions (intersections) will there be in this system of two equations 5x(2) plus y 2x(2) plus y?
Last Answer : None because the given terms of an expression are not equations because there are no equality signs.
Description : Simplify: (i) (a + b + c)2 + (a – b + c)2 (ii) (a + b + c)2 – (a – b + c)2 (iii) (a + b + c)2 + (a – b + c)2 + (a + b – c)2 (iv) (2x + p – c)2 – (2x – p + c)2 (v) (x2 + y2 – z2)2 – (x2 – y2 + z2)2 -Maths 9th
Last Answer : answer:
Description : What is the length of the circles radius for the circle x2 plus y2 169.?
Last Answer : If x^2 plus y^2 = 169 then the center of the circle is at (0, 0)and its radius is the square root of 169 which is 13
Description : Check whether the following are quadratic equations: (i) (x+ 1)2=2(x-3) (ii) x - 2x = (- 2) (3-x) (iii) (x - 2) (x + 1) = (x - 1) (x + 3) (iv) (x - 3) (2x + 1) = x (x + 5) (v) (2x - 1) (x - 3) = (x ... vi) x2 + 3x + 1 = (x - 2)2 (vii) (x + 2)3 = 2x(x2 - 1) (viii) x3 -4x2 -x + 1 = (x-2)3 -Maths 10th
Last Answer : this is the correct answer!
Description : Which two points satisfy y -x2 plus 2x plus 4 and x plus y 4?
Last Answer : Without any equality signs the given expression can't form anyequations and so therefore determining the values of x and y is notpossible.
Description : The centroid of the area between the circle x2 + y2 = 16 and the line x + y = 4 will have the coordinates a.(4, 2) b.(2, 4) c.(2.34, 2.34) d.(1.16, 1.16) e.None of the above
Last Answer : c. (2.34, 2.34)
Description : The x coordinate of the centroid of the area enclosed by the parabolas y = x2 and x = y2 will be a.107 dynes b.0.44 c.0.43 d.0.45 e.0.46
Last Answer : d. 0.45
Description : Let x be the mean of x1, x2,….,xn and y be the mean of y1, y2, ……,yn the mean of z is x1, x2,….,xn , y1, y2, ……,yn then z is equal to -Maths 9th
Last Answer : NEED ANSWER
Last Answer : According to question find the value of z
Description : Find the value of x3 + y3 + z3 – 3xyz if x2 + y2 + z2 = 83 and x + y + z = 15 -Maths 9th
Last Answer : Consider the equation x + y + z = 15 From algebraic identities, we know that (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) So, (x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + xz) From the question, x2 + y2 + z2 ... y3 + z3 - 3xyz = 15(83 - 71) => x3 + y3 + z3 - 3xyz = 15 12 Or, x3 + y3 + z3 - 3xyz = 180
Description : If x sin3|+ y cos3|=sin|cos| and xsin|=ycos|, prove x2+y2=1. -Maths 9th
Last Answer : xsin3θ+ycos3θ=sinθcosθ (xsinθ)sin2θ+(ycosθ)cos2θ=sinθcosθ (xsinθ)sin2θ+(xsinθ)cos2θ=sinθcosθ xsinθ=sinθcosθ x=cosθ Again, ycosθ=xsinθ ycosθ=cosθsinθ y=sinθ Therefore, x2+y2=sin2θ+cos2θ=1.
Description : The point (-1,2) divides the line segment joining the points A(2,5) and B(x,y) in the ratio 3:4, then the value of x2 + y2 is : (a) 27 (b) 28 (c) 29 (d) 30
Last Answer : (c) 29
Description : Solve for x and y: 1/x - 1/y = 1/3, 1/x2 + 1/y2 = 5/9.
Last Answer : Answer: x = 3/2 or -3 and y = 3 or -3/2.
Description : Find (2x – y + 3z) (4x2 + y2 + 9z2 + 2xy + 3yz – 6xz). -Maths 9th
Last Answer : Solution of this question
Description : Center point of circle a.[x1+x2]/2; [y1+y2]/2; [z1+z2]/2 b.[x1-x2]/2; [y1-y2]/2; [z1-z2]/2 c.[x1-x2]; [y1-y2]; [z1-z2] d.[x2-x1]; [y2-y1]; [z2-z1]
Last Answer : a.[x1+x2]/2; [y1+y2]/2; [z1+z2]/2
Description : What does The number 14 in the equation y equals 2x plus 14?
Last Answer : In the straight line equation of y = 2x+14 the slope or gadientis 2 and the y intercept is 14
Description : What are the points of intersection of the line 2x plus 5y equals 4 with the curve y squared equals x plus 4?
Last Answer : If: 2x +5y = 4 then 25y^2 = 4x^2 -16x +16If: y^2 = x +4 then 25y^2 = 25x +100So: 4x^2 -16x +16 = 25x +100Transposing terms: 4x^2 -41x -84 = 0Factorizing the above: (4x+7)(x-12) = 0 meaning x = -7/4 or x =12By substitution into original equation points of intersection:(-7/4, 3/2) and (12, -4)
Description : What are the points of intersection between the line 3x -y equals 5 and the curve 2x squared plus y squared equals 129?
Last Answer : If: 3x-y = 5 then y^2 = (3x_5)^2 => 9x^2 -30x+25If: 2x^2 + y^2 = 129 then y^2 = 129-2x^2So: 9x^2 -30x+25 = 129-2x^2Transposing terms: 11x^2 -30x -104 = 0Factorizing the above: (11x- ... x = 52/11 or x= -2By substituting x into the original equation intersections areat: (52/11, 101/11) and (-2, -11)
Description : What is the solution when y equals 2x plus 1 is a tangent to the circle 5y2 plus 5x2 equals 1?
Last Answer : If y = 2x+1 is a tangent line to the circle 5y^2 +5x^2 = 1 thenthe point of contact is at (-2/5, 1/5) because it has equalroots
Description : What is the value of y when y equals 2x plus 1.25 is a tangent to the curve y squared equals 10x?
Last Answer : If the line y = 2x+1.25 is a tangent to the curve y^2 = 10x thenit works out that when x = 5/8 then y = 5/2
Description : If the equation x2 minus ax plus 2b equals 0 has prime roots where a and b are positive integers then a minus b is equal to?
Last Answer : I think you mean the roots are prime numbers.Let the two roots be primes p and qThen the equation factorises to (x - p)(x - q) = 0 which can beexpanded to give:x² - (p + q)x + pq = 0Which comparing ... = 2(It doesn't matter if the other prime is even (2) or not as itcancels out from a - b.)
Description : What type of lines match these equations 3x plus 2y -5 -2x plus 3y -5?
Last Answer : If you mean 3x+2y = -5 and -2x+3y = -5 then they are straightline equations
Description : Evaluate each of the following using identities: (i) (2x –1x)2 (ii) (2x + y) (2x – y) (iii) (a2b – b2a)2 (iv) (a – 0.1) (a + 0.1) (v) (1.5.x2 – 0.3y2) (1.5x2 + 0.3y2) -Maths 9th
Last Answer : (i) (2x - 1/x)2 [Use identity: (a - b)2 = a2 + b2 - 2ab ] (2x - 1/x)2 = (2x) 2 + (1/x)2 - 2 (2x)(1/x) = 4x2 + 1/x2 - 4 (ii) (2x + y) (2x - y) [Use identity: (a - b)(a + b) = a2 - b 2 ] (2x + y) (2x - ... ) = a2 - b 2 ](1.5 x 2 - 0.3y2 ) (1.5x2 + 0.3y2 ) = (1.5 x 2 ) 2 - (0.3y2 ) 2 = 2.25 x4 - 0.09y4
Description : What are the vertex and x-intercepts of the graph of the function below y x2 - 2x - 24?
Last Answer : Need answer
Description : What is 2x plus 3y equals 17 and 3x minus 2y equals 0.5?
Last Answer : It is a simultaneous equation and when solved its solutions arex = 71/26 and y = 50/13
Description : what is the result of adding the system of equations? 2x + y = 4 3x - y = 6 -General Knowledge
Last Answer : The result of adding the system of equations 2x + y = 4, 3x - y = 6 is 5x = 10.
Description : A student wrote the equations of the lines a and b drawn in the following graph as y =1 and 2x + 3y =6. Is he right? -Maths 9th
Last Answer : Clearly, line a is parallel to X-axis at a distance of 1 unit in positive direction of Y-axis, therefore its equation is y = 1. Also, if we draw the graph of line 2x + 3y = 6, then its graph should intersect X - axis at (3,0 ... Base Height = 1/2 BC AC = 1/2 1 3 / 2 = 3 / 4 sq unit.
Description : Express the equations 2x-y + 6 =0 and 6x + y + 8 = 0, in the matrix equation form.
Last Answer : Express the equations 2x-y + 6 =0 and 6x + y + 8 = 0, in the matrix equation form.
Description : The ratio of the areas of the two triangles formed by the lines representing the equations and 2x – y + 2 = 0 with X axis and the lines with the Y axis is (a) 1 : 2 (b) 2 : 1 (c) 4 : 1 (d) 1 : 4
Last Answer : (c) 4 : 1
Description : . The ratio of the areas of the two triangles formed by the lines representing the equations and 2x – y + 2 = 0 with X axis and the lines with the Y axis is (a) 1 : 2 (b) 2 : 1 (c) 4 : 1 (d) 1 : 4
Description : A pair of linear equations which has a unique solution x = 2, y = -3 is (a) x + y = -1 ; 2x – 3y = -5 (b) 2x + 5y = -11 ; 4x + 10y = -22(c) 2x – y = 1 ; 3x + 2y = 0 (d) x – 4y – 14 = 0 ;5x – y – 13 = 0
Last Answer : (d) x – 4y – 14 = 0 ;5x – y – 13 = 0
Description : How many solutions does the pair of equations y = 0 and y = -5 have? -Maths 10th
Last Answer : y = 0 and y = -5 are Parallel lines, hence no solution.
Description : If = = in the system of equations a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0 Statement 1 : This is the condition for inconsistent equations Statement 2 : There exists infinitely many solutions ... statements are true ? e) S1 only f) S1 and S2 g) S1 and S3 h) S2 only Answer: (d) S2 o
Last Answer : h) S2 only
Description : The pair of equations 3 x + y = 81 , 81 x – y = 3 has (a) no solution (b) unique solution (c) infinitely many solutions (d) x = 2 , y = 1
Last Answer : d) x = 2 , y = 1
Description : If = = in the system of equations a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0 Statement 1 : This is the condition for inconsistent equations Statement 2 : There exists infinitely many ... parallel Which of the above statements are true ? a) S1 only b) S1 and S2 c) S1 and S3 d) S2 only
Last Answer : d) S2 only