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Question

A normal inclined at an angle of π4 to the x-axis of the ellipse x2a2+y2b2=1 is drawn. It meets the major and minor axes in P and Q respectively. If C is the centre of the ellipse then the area of the triangle CPQ is

A
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C
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D
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Solution

The correct option is C
Given ellipse is x2a2+y2b2=1
m=(dydx)(x1,y1)=b2x1a2y1=1 ( since the normal makes an angle π4 with x-axis) b2x1=a2y1(1)
Since P(x1,y1) lies the ellipse, we have b2x21+a2y21=a2b2(2)
From (1) & (2) P=(a2a2+b2,b2a2+b2)
Equation of the normal at P is x – y = a2b2a2+b2 (3)
Area of the CPQ ie the area of the triangle made by the line (3) with the axes is (a2b2)22(a2+b2)

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