1.

The points on the ellipse (x^(2))/(2)+(y^(2))/(10)=1 from which perpendicular tangents can be drawn to the hyperbola (x^(2))/(5)-(y^(2))/(1) =1 is/are

Answer»

`(sqrt((3)/(2)),sqrt((5)/(2)))`
`(sqrt((3)/(2)),-sqrt((5)/(2)))`
`(-sqrt((3)/(2)),sqrt((5)/(2)))`
`(sqrt((5)/(2)),sqrt((3)/(2)))`

Solution :Required points will lie on the INTERSECTION of ellipse `(X^(2))/(2)+(y^(2))/(10)=1` with director circle of hyperbola `(x^(2))/(5)-(y^(2))/(1) =1` i.e. on `x^(2) + y^(2) =4`
`rArr (sqrt(2)cos theta)^(2) + (sqrt(10)sin theta)^(2) =4`
Solving, we GET `sin theta = +- (1)/(2), cos theta = +-(sqrt(3))/(2)`
`:.` Points are `(+-sqrt((3)/(2)),+-sqrt((5)/(2)))`


Discussion

No Comment Found

Related InterviewSolutions