Question

Tangent to the curve `y=x^2+6` at a point `(1,7)` touches the circle `x^2+y^2+16x+12y+c=0 `at a point `Q`, then the coordinates of `Q` are (A) `(-6,-11)` (B) `(-9,-13)` (C) `(-10,-15)` (D) `(-6,-7)`
A. (6, 7)
B. (-6, 7)
C. (6, -7)
D. (-6, -7)

Answer 1

Correct Answer - D
The equation of the tangenty at (1, 7) to the parabola `x^(2)=y-6` is
`x=((y+7)/2)-6or, 2x-y+5=0`
This touches the circle `x^(2)+y^(2)+16x+12y+c=0`. The point of contact is the point of intersection of `2x-y=0` and a line passing through the centre of the circle parependicular to this line, The equation of that line is x + 2y + 20 = 0.
Hence, the coordinates of the required point are (-6, -7).