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Let 5x-3y=8sqrt2 be normal at P(5/(sqrt(...

Let `5x-3y=8sqrt2` be normal at `P(5/(sqrt(2)),3/(sqrt(2)))` to an ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1, a > b.` If `m,m'` are feet of perpendiculars from foci `s,s'` respectively. or tangents at p, then point of intersection of `sm' and s'm` is

A

`((5)/(2),0)`

B

`(0,(5)/(2))`

C

`((41)/(10sqrt(2)),(3)/(2sqrt(2)))`

D

`((3)/(2sqrt(2)),(41)/(10sqrt(2)))`

Text Solution

Verified by Experts

The correct Answer is:
C
SM' and S'M intersect at mid-point of PG (where G is point of intersection of normal at P with major axis)
`G ((8sqrt(2))/(5),0)`
Mid-point of `PG ((41)/(10sqrt(2)),(3)/(2sqrt(2)))`
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