Question

find the equation to the hyperbola referred to its axes as axis of coordinates whose semi conjugate axis is 5 and which passes through the point 2, - 1

Answer 1

Answer:

13x² - 2y² = 50

Step-by-step explanation:

Hi,

Equation to hyperbola with axes as axis of coordinates is

x²/a² - y²/b² = 1, where a is semi transverse axis and b is semi

conjugate axis.

Given that b = 5

Hence equation of hyperbola would become

x²/a² - y²/5² = 1

Given that hyperbola passes through (2, -1), hence

4/a² - 1/25 = 1

4/a² = 26/25

a² = 100/26

a² = 50/13

Hence , the equation of the hyperbola will be x²/(50/13) - y²/25 = 1

or

13x² - 2y² = 50 is the required equation of the hyperbola.

Hope, it helps !