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The locus of the point which divides the...

The locus of the point which divides the double ordinates of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` in the ratio `1:2` internally is

A

`(x^(2))/(a^(2))+(9y^(2))/(b^(2))=1`

B

`(x^(2))/(a^(2))+(9y^(2))/(b^(2))=(1)/(9)`

C

`(9x^(2))/(a^(2))+(9y^(2))/(b^(2))=1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A

Let `P-=(a cos theta, b sin theta),Q-=(a co theta,-b sin theta)`
`PR:RQ=1:2`
`:. h=a cos theta`
or `cos theta=(h)/(a)" "(1)`
or `k=(b)/(3) sin theta`
or `sin theta=(3k)/(b)" "(2)`
On squaring and adding (1) and (2), we get
`(x^(2))/(a^(2))+(9y^(2))/(b^(2))=1`
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