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A line passing through the origin O(0,0)...

A line passing through the origin `O(0,0)` intersects two concentric circles of radii `aa n db` at `Pa n d Q ,` If the lines parallel to the X-and Y-axes through `Qa n dP ,` respectively, meet at point `R ,` then find the locus of `Rdot`

Text Solution

Verified by Experts

Let `R-=(h,k)`
From the fiugure,
`h=a cos theta`
and `k=b sin theta`

Squaring and adding, we get
`(h^(2))/(a^(2))+(k^(2))/(b^(2))=1`
So, `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` is required locus.
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