Question

A straight line with slope 2 and y-intercept 5 touches the circle, $x^2+y^2+16x+12y+c=0$ at a point Q. Then the co-ordinates of Q are

• A. $(-6,11)$
• B. $(-9,-13)$
• C. $(-10,-15)$
• D. $(-6,-7)$

Answer 1

The correct option is D $(-6,-7)$

Equation of the line is

$y=2x+5$

From the equation of a circle, we have center $=(-8,-6)$

let the point of contact be $(x_1,y_1)$

$y_1=2x_1+5$ and $\frac{y_1+6}{x_1+8}\times 2=-1$ (both lines are perpendicular)

$\Rightarrow x_1=-6$ and $y_1=-7$