Find the foci of the hyperbola.
-$4 y ^ { 2 } - 25 x ^ { 2 } = 100$
A) $( 0 , \sqrt { 29 } ) , ( 0 , - \sqrt { 29 } )$
B) $( \sqrt { 21 } , 0 ) , ( - \sqrt { 21 } , 0 )$
C) $( 0 , \sqrt { 21 } ) , ( 0 , - \sqrt { 21 } )$
D) $( \sqrt { 29 } , 0 ) , ( - \sqrt { 29 } , 0 )$

Question

Quizplus · Accepted Answer

The equation of the hyperbola is given in the form $4y^2 - 25x^2 = 100$. To find the foci, we first rewrite the equation in standard form: $\frac{y^2}{25} - \frac{x^2}{4} = 1$. The foci are located at $(0, \pm c)$ for a hyperbola that opens up and down. We find $c$ using $c^2 = a^2 + b^2$, where $a^2 = 25$ and $b^2 = 4$, giving $c^2 = 29$. Thus, the foci are $(0, \pm \sqrt{29})$.

Find the Foci of the Hyperbola 4y2−25x2=1004 y ^ { 2 } - 25 x ^ { 2 } = 1004y2−25x2=100

Find the Foci of the Hyperbola $4 y ^ { 2 } - 25 x ^ { 2 } = 100$