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If the tangents on the elipse 4x^(2)+y^(...

If the tangents on the elipse `4x^(2)+y^(2)=8` at the points `(1,2)` and `(a,b)` are perpendicular to each other, them `a^(2)` is equal to:

A

`64/17`

B

`4/17`

C

`2/17`

D

`182/17`

Text Solution

Verified by Experts

The correct Answer is:
C
Slope of the tangent at `(x_1,y_1) ` for ellipse `x^2/2+y^2/8=1 " is " -8/2xxx_1/y_1=-4x_1/y_1`
`:.` Slope of tangent at (1,2) is –2
Perpendicular tangents slope will be 1/2
Slope of tangent at `(a cos theta, b sin theta)`
For `x^2/a^2+y^2/b^2=1 " is " -b/acottheta=-2cottheta`
`implies-2cottheta=1/2,cottheta=-1/4rArrcostheta=pm1/(sqrt(17))`
`impliesa^2=(sqrt(2)costheta)^2=2cos^2theta=2/17`
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