Write an equation for the hyperbola.
-A nuclear cooling tower cross section is a hyperbola having a diameter of $60 \mathrm { ft }$ at the center. The distance between the two foci is $92 \mathrm { ft }$. What is the equation for the hyperbola?
A) $\frac { x ^ { 2 } } { 900 } - \frac { y ^ { 2 } } { 1216 } = 5$

B) $\frac { x ^ { 2 } } { 900 } - \frac { y ^ { 2 } } { 1218 } = 1$

C) $\frac { x ^ { 2 } } { 900 } - \frac { y ^ { 2 } } { 2116 } = 1$

D) $\frac { x ^ { 2 } } { 900 } - \frac { y ^ { 2 } } { 1216 } = 1$

Question

Write an equation for the hyperbola.
-A nuclear cooling tower cross section is a hyperbola having a diameter of $60 \mathrm { ft }$ at the center. The distance between the two foci is $92 \mathrm { ft }$. What is the equation for the hyperbola?
A) $\frac { x ^ { 2 } } { 900 } - \frac { y ^ { 2 } } { 1216 } = 5$

B) $\frac { x ^ { 2 } } { 900 } - \frac { y ^ { 2 } } { 1218 } = 1$

C) $\frac { x ^ { 2 } } { 900 } - \frac { y ^ { 2 } } { 2116 } = 1$

D) $\frac { x ^ { 2 } } { 900 } - \frac { y ^ { 2 } } { 1216 } = 1$

Quizplus · Accepted Answer

The equation of a hyperbola in standard form is $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, where $2a$ is the length of the transverse axis (diameter in this case, which is 60 ft, so $a = 30$ ft) and $2c$ is the distance between the foci (92 ft, so $c = 46$ ft). Using the relationship $c^2 = a^2 + b^2$, we find $b^2 = c^2 - a^2 = 46^2 - 30^2 = 2116 - 900 = 1216$. Therefore, the correct equation is $\frac{x^2}{900} - \frac{y^2}{1216} = 1$.

Write an Equation for the Hyperbola 60ft60 \mathrm { ft }60ft

Write an Equation for the Hyperbola $60 \mathrm { ft }$