Question

Let P1 be a parabola with vertex (3, 2) and focus (4, 4) and P2 be its mirror image with respect to the line x + 2y = 6. Then the directrix of P2 is x + 2y = _______.

Answer 1

The correct answer is 10
Focus = (4, 4) and vertex = (3, 2)
∴ Point of intersection of directrix with axis of parabola = A = (2, 0)
Image of A(2, 0) with respect to line
x + 2y = 6 is B(x2, y2)
$∴\frac{x^2−2}{1}=\frac{y^2−0}{2}=\frac{−2(2+0−6)}{5}$
$∴B(x_2,y_2)=(185,165).$
Point B is point of intersection of direction with axes of parabola P2.
∴ x + 2y = λ must have point
$(\frac{18}{5},\frac{16}{5})$
∴ x + 2y = 10