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Question

# The equation of reflection of the ellipse (x−4)216+(y−3)29=1 about the line x−y−2=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 (x−5)29+(y−2)216=1Given : (x−4)216+(y−3)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 x−y−2=0 is h−4(1+cosθ)1=k−3(1+sinθ)−1=−2[4(1+cosθ)−3(1+sinθ)−2]2=1−4cosθ+3sinθ So, ⇒h=5+3sinθ, k=2+4cosθ⇒(h−53)2+(k−24)2=1 Hence, the equation of reflected ellipse is (x−5)29+(y−2)216=1

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