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On the ellipse 4x^2+9y^2=1, the points a...

On the ellipse `4x^2+9y^2=1,` the points at which the tangents are parallel to the line `8x=9y` are (a) `(2/5,1/5)` (b) `(-2/5,1/5)` `(-2/5,-1/5)` (d) `(2/5,-1/5)`

A

`(2//5, 1//5)`

B

`(pm 2//5, pm 1//5)`

C

`(-2//5, -1//5)`

D

`(pm2/5, pm 1//5)`

Text Solution

Verified by Experts

The correct Answer is:
B
We have, `a^(2) = 1/4, b^(2) = 1/9, m = 8/9`
The required points are
`(pm (a^(2)m)/(sqrt(a^(2)m^(2) + b^(2))), pm (b^(2))/(sqrt(a^(2)m^(2) + b^(2)))) = (pm 2/5, pm 1/5)`
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