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The maximum distance of the centre of th...

The maximum distance of the centre of the ellipse `(x^(2))/(16) +(y^(2))/(9) =1` from the chord of contact of mutually perpendicular tangents of the ellipse is

A

`(144)/(5)`

B

`(9)/(5)`

C

`(16)/(5)`

D

`(8)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
C

Perpendicular tangents meet on director circle `x^(2) + y^(2) = 25`, Any point on this circle is `P(5 cos theta, 5 sin theta)`
Equation of chord of contact of ellipse w.r.t this point is
`(5 cos theta x)/(16) + (5 sin theta y)/(9) =1`
Distance from center `= (1)/(sqrt((25)/(256)cos^(2)theta+(25)/(81)sin^(2)theta))`
For maximum value `cos theta =1` and `sin theta = 0`
Maximum distance `= (16)/(5)`
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