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Question

Let an ellipse and a hyperbola have same foci. If the length of conjugate axis of the hyperbola is equal to the length of minor axis of the ellipse, then the value of 1e21+1e22 is (e1 and e2 denote the eccentricities of the two conics)

A
1
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B
4
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C
3
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D
2
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Solution

The correct option is D 2
x2a21+y2b21=1, a1>b1

x2a22y2b22=1

(±a1e1,0)(±a2e2,0)
a1e1=a2e2 (1)

Also, 2b1=2b2
b1=b2
b21=b22
a21(1e21)=a22(e221)
a22e22e21(1e21)=a22(e221) [From (1)]
1e211=11e22
1e21+1e22=2

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