InterviewSolution
Saved Bookmarks
| 1. |
Two tangents to the hyperbola (x^(2))/(25) -(y^(2))/(9) =1, having slopes 2 and m where (m ne 2) cuts the axes at four concyclic points then the slope m is/are |
|
Answer» `-(1)/(2)` It meets the axis at `A -= (+-(sqrt(91))/(2),0),B (0,+-sqrt(91))` Tangents having slope `'m', y = MX+- sqrt(25 m^(2)-9)` It meets the axis at `D(+-(sqrt(25m^(2)-9))/(m),0), C -= (0,+-sqrt(25m^(2)-9))` ABCD is cyclic quadrilateral `rArr OA XX OD xx OB xx OC` `rArr (sqrt(91)(sqrt(25m^(2)-9)))/(2m) =sqrt(91) (sqrt(25m^(2)-9))` `rArr 2m = 1 rArr m= (1)/(2)` |
|