Thread: need help on hyperbola

find the equation of the hyperbola:
center at (0,0) transverse axis along the x-axis, passing through the points (3,5), (2,-3).

Originally Posted by ^_^Engineer_Adam^_^

find the equation of the hyperbola:
center at (0,0) transverse axis along the x-axis, passing through the points (3,5), (2,-3).

Hi,

the general equation of such a hyperbola is:

x²/a² - y²/b² = 1 with a and b as the semi-axes.

You know the coordinates of 2 points which must satisfy this equation:

i) 9/a² - 25/b² = 1

ii) 4/a² - 9/b² = 1

From i) you get

iii) a² = (9b²)/(b² + 25).

Plug this term for a² into the equation at ii):

4/((9b²)/(b² + 25)) - 9/b² = 1. Solve for b².

I've got b² = 19/5. Substitute this value into the equation at iii). You'll get

a² = 19/16.

The equation of the hyperbola becomes:

x²/(19/16) - y²/(19/5) = 1 <===> (16x²)/19 - (5y²)/19 = 1

EB