write the equation of the hyperbola whose center is at the o

Solution

General equation of hyperbola with centre at origin and vertical transverse axis is

(y²/a²) - (x²/b²) = 1

Given equations of asymptotes are 6x + 2y = 0 , 6x - 2y = 0

we have equations of asymptotes as y = (a/b)x , -(a/b)x

==> 2y = 6x

==> y = 6x / 2

==> y = 3x

==> y = (3/1)x

==> a = 3 , b = 1

==> Equation of hyperbola is (y²/3²) - (x²/1²) = 1

==> (y²/9) - x² = 1

==> y² - 9x² = 9

==> 9x² - y² + 9 = 0 is the required equation of hyperbola