The maximum distance of the centre of the ellipse `x^2/(81)+y^2/(25)=1` from a normal to the ellipse is

Explanation

let us take a point as `(9cos theta , 5sin theta)`

the tangent on the point will be ` (x*9cos theta)/81 + (y*5*sin theta)/25 = 1 `

`(x*Cos theta)/9 + (y*sin theta)/5 = 1`

`y= (-5*cos theta)/(9*sin theta)* x + 5/ sin theta`

so slope will be `(5Cos theta)/ (9 sin theta)`

as we know that, slope of tangent * slope of normal = -1

so, slope of normal is `(9*Sin theta)/(5*cos theta)`

for normal `y- sin theta = (9*sin theta)/(5* cos theta) * (x- 9*cos theta)`

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