Question

Show that the equation x2 − 4y2 +8y − 20 = 0 represent standard form hyperbola.

Answer 1

The equation x^2 - 4y^2 + 8y - 20 = 0 represents a standard form hyperbola.

Step-by-step explanation:

The given equation, x2 - 4y2 + 8y - 20 = 0, can be rearranged as (x2 - 4y2) + 8y = 20.

By completing the square, we get (x2 - 4y2) + 8y + 4 = 24.

Now, we can rewrite it as (x - 0)2 - 4(y - 1)2 = 24.

This equation represents the standard form of a hyperbola, where the center is at (0, 1) and the shape of the hyperbola is determined by the coefficients of the squared terms.