1.

If foci of an ellipse are (-2,3),(5,9) & 2x+3y+15=0 is tangent to the ellipse. Then find the point of contact the tangent cannot be

Answer»

`((7)/(2),-1)`
`(-(9)/(2),-2)`
`(-1,(9)/(2))`
`(-1,(7)/(2))`

SOLUTION :As we know that the ray PASSING thorugh on FOCUS will pass through the another after reflection So point `S_(1)` P. `S_(2)^(')` will be collinear.
where `S_(2)^(')` is the point of reflection of `S_(2)` inL.
`S_(2)^(')=(-11,-15)`
So line joining `S_(1)&S_(2)^(')` is given by
`(y-3)=2(x+2)`
`y-3=2x+4`
`2x-y+7=0`
So point `P` will be the point of intersection of
`2x-y+7=0&2x+3y+15=0`
so point P will be the point of intersection of `2x-y+7=0&2x+3y+15=0`
i.e., `(-(9)/(2),-2)`


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