Find an equation for the hyperbola that satisfies the given conditions.
Asymptotes: y = ±x,
hyperbola passes through (5, 3)

The equation of hyperbola that satisfies the given conditions is and this can be determined by using the given data.

Given :

The generalized equation of Hyperbola is given below:

  --- (1)

So, according to the data, the asymptotes: y = ±x. Therefore, the slope is:

a = b

The value of h = 0 and k = 0 in the equation (1).

Now, in order to determine the value of 'a' use the below calculation.

Now, substitute the value of y and x in the above equation.

25 - 9 =

a = 4

So, the value of 'b' is also equal to 4.

Now, substitute the values of the known terms in the equation (1).

For more information, refer to the link given below:

link

Step-by-step explanation:

The slope of the one of the asymptotes is:

The form of the asymptotes indicates that the hyperbola is centered at origin. Therefore, the equation of the conic is simplified into this form:

The equation of the hyperbola is:

it would be 6xy and -16xy.