What is 3a squared when a equals to -3?

What is 3a squared when a equals to -3?
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6
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What are the points of intersection of the line 2x plus 5y equals 4 with the curve y squared equals x plus 4?

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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)

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What are the points of contact when the line x -y equals 2 crosses the curve x squared -4y squared equals 5 showing work?

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Last Answer : If: x -y = 2 then x^2 = (2+y)^2 => 4+4y+y^2If: x^2 -4y^2 = 5 then x^2 = 5+4y^2So: 5+4y^2 = 4+4y+y^2Transposing terms: 3y^2 -4y +1 = 0Factorizing the above: (3y-1)(y-1) = 0 meaning y = 1/3 or y =1By substitution contacts are made at: (7/3, 1/3) and (3, 1)

What are the points of intersection between the line 3x -y equals 5 and the curve 2x squared plus y squared equals 129?

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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)

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Last Answer : If y = 3x + 1 is a tangent to x² + y² = k (k > 0 since it isa square), then where they meet has a repeated root; they meetat:x² + (3x + 1)² = k→ x² + 9x² + 6x + 1 - k = 0→ 10x² + 6x + (1 - k) = 0This is the ... 3/10→ y = 3 -3/10 + 1 = 9/10 + 1 = 1/10→ point of contact is (-3/10, 1/10) with k = 1/10

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Last Answer : There is a hint to how to solve this in what is required to be shown: a and b are both squared.Ifa cos θ + b sin θ = 8a sin θ - b cos θ = 5then square both sides of each to get:a² cos² θ + 2ab cos ... + sin² θ) + b² (sin² θ + cos² θ) = 89using cos² θ + sin² θ = 1â†' a² + b² = 89

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