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Question

If the normal at any point P on the ellipse x29+y216=1 meets the axes at G and g, respectively, then the ratio of PG:Pg is


Your Answer
A
3:4
Your Answer
B
4:3
Your Answer
C
9:16
Correct Answer
D
16:9 

Solution

The correct option is D 16:9 
Let P(acosθ,bsinθ) be a point on the ellipse x2a2+y2b2=1.
Then the equation of the normal at P is axsecθby cosec θ=a2b2.
It meets the axes at G(a2b2acosθ,0) and g(0,a2b2asinθ)

PG2=(acosθa2b2acosθ)2+(bsinθ0)2
            =b2a2(b2cos2θ+a2sin2θ)
Pg2=a2b2(b2cos2θ+a2sin2θ)

PG2:Pg2=b4:a4
PG:Pg=b2:a2
PG:Pg=16:9 

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