The tangent and normal to the ellipse 3x2+5y2=32 at the point P(2,2) meet the xāaxis 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 D6815 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, (y−2)=−35(x−2) ⇒3x+5y=16 Q=(163,0)
Equation of normal at (2,2) is, (y−2)=53(x−2) ⇒5x−3y=4 R=(45,0)