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The area of the rectangle formed by the ...

The area of the rectangle formed by the perpendicular from the center of the standard ellipse to the tangent and normal at its point whose eccentric angle is `pi/4`, is

Text Solution

Verified by Experts

The correct Answer is:
`(30)/(13)` sq. units
Equation of tangent at point `P((pi)/(4))` is
`(x)/(3)cos.(pi)/(4)+(y)/(2)sin.(pi)/(4)=1`
or `2x+3y-6sqrt(2)=0`
Equation of normalat P is
`3sqrt(2)x-2sqrt(2)y-5=0`
Distacne of centre from the tangent is `(6sqrt(3))/(sqrt(13))`
Distance of centre from the normal is `(5)/(sqrt(2)sqrt(13))`
`:.` Area of required rectangle `=(6sqrt(2))/(sqrt(13))xx(5)/(sqrt(2)sqrt(13))=(30)/(13)` sq. unit
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