What is equation of hyperbola given Transverse axis on the y-axis, (2, √2) and (0, -1) are points on the curve?

1 Answer
Aug 3, 2018

x^2/4-y^2=-1, or, 4y^2-x^2=4x24y2=1,or,4y2x2=4.

Explanation:

We are given that the Transverse Axis of the required

Hyperbola is on the Y-"Axis"YAxis.

So, we suppose that its equation is S : x^2/a^2-y^2/b^2=-1S:x2a2y2b2=1.

(2,sqrt2) in S. :. 2^2/a^2-(sqrt2)^2/b^2=-1, or,

4/a^2-2/b^2=-1...............(ast_1).

Again, (0,-1) in S rArr -1/b^2=-1, i.e., b^2=1.................(ast_2).

(ast_2) & (ast_1) rArr 4/a^2=2/b^2-1=1rArr a^2=4...(ast_3).

(ast_2) and (ast_3) give the desired equation of the hyperbola as

S : x^2/4-y^2=-1, or, 4y^2-x^2=4.