Q.

Let P be any point on the curve  9x2+16y2−144=0, but not on the axes. Let M,N be the feet of the perpendiculars drawn from P on minor and major axes respectively . Let the tangent at P cuts minor and major axes at R,T respectively. Let the normal at P cuts major axis at G and CF be the perpendicular from centre C to the normal at P. Then, which of the following is/are true?

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a

PF. PG = 16

b

PF. PG = 9

c

PM. CT = 16

d

PN. CR = 9

answer is B.

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Detailed Solution

P(4cos⁡θ,3sin⁡θ); Tangent at P is x4cos⁡θ+y3sin⁡θ=1 Normal at p is 4xcos⁡θ−3ysin⁡θ=7, CM=PN=3sin⁡θ,CT=4cos⁡θG74cos⁡θ,0CN=PM=4cos⁡θ,CR=3sin⁡θ   option2:PF.PG=b2 =9 since PF.PG=b2 option3: PM.CT=4cosθ.4cosθ=16option4:PN.CR=3sinθ.3sinθ=9
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