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Question

The equation of reflection of the ellipse (x4)216+(y3)29=1 about the line xy2=0 is
​​​​​​​(correct answer + 1, wrong answer - 0.25)

A
(x2)216+(y5)29=1
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B
(x2)29+(y5)216=1
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C
(x5)216+(y2)29=1
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D
(x5)29+(y2)216=1
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Solution

The correct option is D (x5)29+(y2)216=1
Given : (x4)216+(y3)29=1

Any point P on the curve is
P=(4(1+cosθ), 3(1+sinθ))
Let the reflection of P be (h,k)

Now, the reflection of the point P about the line xy2=0 is h4(1+cosθ)1=k3(1+sinθ)1=2[4(1+cosθ)3(1+sinθ)2]2=14cosθ+3sinθ

So,
h=5+3sinθ, k=2+4cosθ(h53)2+(k24)2=1

Hence, the equation of reflected ellipse is
(x5)29+(y2)216=1

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