If a tangent on ellipse at A(1,1) inters...

If a tangent on ellipse at `A(1,1)` intersect its directrix at `B(7,-6)` and `S` be the focus of ellipse and `C(alpha, beta)` is the centre of `/_\SAB`, then

`alpha+beta=1`

`alpha-beta=7`

`SC^(2)=20.5`

`SC^(2)=21.25`

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Verified by Experts

The correct Answer is:

A, B, D

`:' /_\SAB` is right angle at `S`
Centre `C` is `((1+7)/2, (1-6)/2)=(4,-3)`
`:. alpha=4` and `beta=-3`
`:. alpha+beta=1` and `alpha-beta=7`
SC is radius and `AB` is diameter
`:. SC=1/2 sqrt(36+49)=1/2 sqrt(85)=sqrt(85/4)=sqrt(21.25)`

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