What is the center and the radius of the circle x2 plus y2 -4x -6y -3 equals 0?

What is the center and the radius of the circle x2 plus y2 -4x -6y -3 equals 0?
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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
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Related questions

What is the equation of the tangent line that meets the circle x2 -4x plus y2 -6y equals 4 at the point 6 4?

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

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?

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

What is the center and the radius of the circle x2 plus y2 equals 12x -10y -12?

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

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?

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

What is the length of the circle radius if the circle is x2 plus y2 equals 1?

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

What is the length of the tangent line from the point 9 0 to the circle x2 plus 8x plus y2 -9 equals 0?

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

What is the point of contact when the line y equals 2x meets the circle x2 plus y2 -8x -y plus 5 equals 0?

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)

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?

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

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?

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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)

What is the length of the circles radius for the circle x2 plus y2 169.?

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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

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Last Answer : If: y = -2x then y ^2 = 4x^2If: x^2 + y^2 = 80 then x^2 +4x^2 = 80So: 5x^2 = 80Divide all terms by 5: x^2 = 16Square root both sides: x = -4 or +4By substitution into the original equation solutions are: (-4,8) and (4, -8)

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