Question

Find the equation for the hyperbola with center at the origin, one vertex at (6, 0), and a focus at (10, 0).

	A.	(x2/64) – (y2/36) = 1
	B.	(x2/36) – (y2/64) = 1
	C.	(x2/64) + (y2/36) = 1
	D.	(x2/36) + (y2/64) = 1

 

Answer 1

Vertex : (a, 0) = (6, 0)  ----->   a = 6.

Focus : (c, 0) = (10, 0)  ----->   c = 10.

Center : (h, k) = (0, 0).

Since the y - coordinate is same in the vertex and focus this is horizontal hyperbola.

The horizontal hyperbola equation is x²/a² - y²/b² = 1.

The relation between a, b and c is b² = c² - a².

Substitute a = 6 and c = 10 in the equation b² = c² - a².

b² = 10² - 6²

b² = 100 - 36

b² = 64

b = ± 8.

Substitute a = 6 and b = 8 in the hyperbola equation x²/a² - y²/b² = 1.

x²/6² - y²/8² = 1

x²/36 - y²/64 = 1

The option B is correct.