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  • If the tangent at (1,7) to the curve  touches the circle <img alt="\mathrm{x

If the tangent at (1,7) to the curve \mathrm{x^2=y-6} touches the circle \mathrm{x^2+y^2+16 x+12 y+c=0}, then the value of \mathrm{ \frac{c}{19}} is

Option: 1

6


Option: 2

5


Option: 3

7


Option: 4

8


Answers (1)

best_answer

\mathrm{\text { The equation of tangent at }(1,7) \text { to } x^2=y-6 \text { is }} 2x – y + 5 = 0

The perpendicular distance of centre (–8, –6) to the line 2x – y + 5 = 0 should be equal to the radius of the circle.

\mathrm{\begin{aligned} & \therefore \sqrt{64+36-c}=\frac{|-16+6+5|}{\sqrt{5}} \\ & \Rightarrow \sqrt{5}=\sqrt{100-c} \Rightarrow c=95 \end{aligned}}

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