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Question

The tangent and normal to the ellipse 3x2+5y2=32 at the point P(2,2) meet the xāˆ’axis at Q and R, respectively. Then the area (in sq. units) of the triangle PQR is :

A
3415
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B
163
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C
143
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D
6815
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Solution

The correct option is D 6815
Given,
Equation of ellipse 3x2+5y2=32
Diffrentiating both sides
6x+10yy=0
y=3x5y
y(2,2)=35

Equation of tangent at (2,2) is,
(y2)=35(x2)
3x+5y=16
Q=(163,0)

Equation of normal at (2,2) is,
(y2)=53(x2)
5x3y=4
R=(45,0)

QR=(16345)2=(6815)2=6815 and height =2

Area=12×(QR)×2=QR=6815


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