InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Find the equations of the hyperbola satisfying the given conditions :Foci `(0,+-sqrt(10))`, passing through (2,3) |
|
Answer» Here, Foci of hyperbola `= (+-sqrt10,0)` That means the transverse axis of the hyperbola is `Y`-axis. So, the equation will be of the type, `y^2/a^2-x^2/b^2 = 1->(1)` Also, `c = sqrt10` In a hyperbola, `c^2 = a^2+b^2` Putting value of `c`, `=> (sqrt10)^2 = a^2+ b^2` `=>b^2 = 10-a^2` Putting vallue of `b^2` in (1), `y^2/a^2-x^2/10-a^2 = 1->(2)` As hyperbola is passing through `(2,3)`, `x=2` and `y=3` should satisfy (2). `So, 9/a^2-4/(10-a^2) = 1` `=>9(10-a^2)-4a^2 = a^2(10-a^2)` `=>90-9a^2-4a^2 = 10a^2 - a^4` `=>a^4-23a^2+90 = 0` `=>a^4-18a^2-5a^2+90 = 0` `=>(a^2-18)(a^2-5) = 0` `=> a^2 = 18 and a^2 = 5` But, `a^2` can not be greater than `c^2`. `:.a^2 = 5` `b^2 = 10 - 5 = 5` Putting values of `a^2` and `b^2` in (1), `y^2/5-x^2/5 = 1` |
|