Question

The straight line x-2y+1=0 intersects the circle $x^2+y^2=25$ at points A and B, then the coordinates of points of intersection of tangents drawn at A and B are

• A. (-25,50)
• B. (25,-50)
• C. (-5,25)
• D. (5,-25)

Answer 1

The correct option is A (-25,50)

Let C (h,k) be the intersection point of the tangents drawn at A and B. Then AB will be the chord of contact of the tangents drawn from C to the circle $x^2+y^2=25$.
So the equation of the chord of contact is hx + ky - 25 = 0
comparing the above equation with the given equation of AB: x - 2y + 1 = 0, we get
$\Rightarrow \frac{h}{1}=\frac{k}{-2}=\frac{-25}{1}\Rightarrow h=-25,k=50$