Write an equation for the hyperbola.
-$x$-intercept 4 ; center at origin; passing through $( 4 \sqrt { 5 } , 6 )$
A) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$
B) $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 36 } = 1$
C) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$
D) $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$

Question

Quizplus · Accepted Answer

The hyperbola has a horizontal transverse axis with x-intercept 4, so $\frac{x^2}{16}$ is correct. It passes through $(4\sqrt{5}, 6)$, satisfying $\frac{(4\sqrt{5})^2}{16} - \frac{6^2}{b^2} = 1$, which confirms choice D.

Write an Equation for the Hyperbola xxx -Intercept 4 ; Center at Origin; Passing Through

Write an Equation for the Hyperbola $x$ -Intercept 4 ; Center at Origin; Passing Through