Question

The circle `x^2 + y^2 - 2x - 6y+2=0` intersects the parabola `y^2 = 8x` orthogonally at the point `P`. The equation of the tangent to the parabola at `P` can be
A. x-y-4=0
B. 2x+y-2=0
C. x+y-4=0
D. 2x-y+1=0

Answer 1

Correct Answer - D
Let `y=mx+2/m" be a tangent to "y^(2)=8x.` Since the circle `x^(2)+y^(2)-2x -6y+2=0` interscts the parabola `y^(2) = 8x` through the centre of the circle i.e. (1, 3).
`:." "3=m+2/mrArrm^(2)-3m+2=0rArrm=1,2`
Thus, the equations of tangents are
`y=x+2" and "2x-y+1=0.`