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

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Answer 1 · 2018-08-03T07:27:54

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

We are given that the Transverse Axis of the required

Hyperbola is on the #Y-"Axis"#.

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