Hyperbola 2 Question 15

15.

The line 2x+y=1 is tangent to the hyperbola x2a2y2b2=1. If this line passes through the point of intersection of the nearest directrix and the X-axis, then the eccentricity of the hyperbola is……

(2010)

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Answer:

Correct Answer: 15. (2)

Solution:

  1. On substituting ae,0 in y=2x+1, we get

0=2ae+1ae=12

Also, y=2x+1 is tangent to hyperbola.

1=4a2b21a2=4(e21)4e2=5e2e45e2+4=0(e24)(e21)=0e=2,e=1

e=1 gives the conic as parabola. But conic is given as hyperbola, hence e=2.



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