What Is the Equation of the Curve Reflected Over the Line x-y-2=0?

[utkarshakash]

Homework Statement

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.

Homework Equations

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.

 

[Saitama]

Homework Statement

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.

Homework Equations

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.

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?