Equation of reflected curve

  • #1
utkarshakash
Gold Member
855
13

Homework Statement


Find equation of the curve on reflection of the ellipse [itex]\dfrac{(x-4)^2}{16} + \dfrac{(y-3)^2}{9} = 1 [/itex] 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).

[itex]\dfrac{4+4cos \theta + h}{2} - \dfrac{3+3sin \theta + k}{2} - 2 =0[/itex]

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

Answers and Replies

  • #2
3,816
92

Homework Statement


Find equation of the curve on reflection of the ellipse [itex]\dfrac{(x-4)^2}{16} + \dfrac{(y-3)^2}{9} = 1 [/itex] 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).

[itex]\dfrac{4+4cos \theta + h}{2} - \dfrac{3+3sin \theta + k}{2} - 2 =0[/itex]

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?
 

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