Question

The circle x² +y² –2x–6y+2 = 0 intersects the parabola y² = 8x orthogonally at the point P. The equation of the tangent to the parabola at P can be

a. 2x –y+1 = 0

b. 2x+y –2 = 0

c. x+y –4 = 0

d. x –y –4 = 0

Answer 1

Correct option is a. 2x –y+1 = 0

: Let y = mx + 2/m be tangent to y² = 8x. Since circle intersects the parabola orthogonally. So this tangent is the normal for the circle. Every normal of the circle passes through its centre. So centre (1, 3).

3= m+ 2/m

m² – 3m+2= 0

(m – 2) (m – 1) = 0

m = 1, 2.

y = x+2 or y = 2x+1