# Equation of reflected curve

1. Nov 27, 2013

### utkarshakash

1. The problem statement, all variables and given/known data
Find equation of the curve on reflection of the ellipse $\dfrac{(x-4)^2}{16} + \dfrac{(y-3)^2}{9} = 1$ about the line x-y-2=0.

2. Relevant equations

3. The attempt at a solution
Let the general point be P(4+4cosθ,3+3sinθ). Let the reflected point be (h,k).

$\dfrac{4+4cos \theta + h}{2} - \dfrac{3+3sin \theta + k}{2} - 2 =0$

I need one more condition so that I can eliminate theta.

2. Nov 27, 2013

### Pranav-Arora

Why not find the reflection of the point (4+4cosθ,3+3sinθ) about the given line? It gives h and k in terms of $\theta$ and its very straightforward from there.

Use the condition that line joining (h,k) and P is perpendicular to x-y-2=0. Can you take it from here?