Question

at which point the tangent at 1, 7 to the curve x square equal to by -6 touches the circle X square + Y square + 16 X + 12 Y + C is equal to zero​

Answer 1

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Answer 2

$\large\underline\mathrm\red{Solution}$

• The tangent at (1 , 7) to the parabola x² = y - 6x

x(1) = 1/2 (y + 7) - 6

2x = y + 7 - 12

y = 2x + 5

$\large\mathrm\red{Thus}$, tangent to the circle

x² + y² + 16x + 12y + c = 0

x² + (2x + 5)² + 16x + 12(2x + 5) + c = 0

5x² + 60x + 85 + c = 0

α + β = -60/5

α = -6

x = -6

y = 2x + 5

= 2 × -6 + 5

= 12 - 5

= -7

$\large\mathrm\red{Point \: of \: contact \: is \: (-6, -7)}$

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