Question

What are the foci of the hyperbola given by the equation (x+10)^2/25 - (y+1)^2/9= 1?

Answer 1

\[\frac{ (x+10)^2 }{ 25 } - \frac{ (y+1)^2 }{ 9 } = 1\]

Answer 2

^^^What are the foci of the hyperbola given by the equation??^^^

Answer 3

first find the center
the center of \[\frac{ (x-h)^2 }{ a^2 } - \frac{ (y-k)^2 }{ b^2 } = 1\] is \((h,k)\)

Answer 4

then the foci are found to be \(\sqrt{a^2+b^2}\) units to the left and right of the center

Answer 5

in your case \(\sqrt{a^2+b^2}=\sqrt{25+9}=\sqrt{34}\)

Answer 6

you good from there?

Answer 7

Sorta, these are the answer choices,
(-1 ±√34 , -10)

(-1, -10 ± √34 )

(-10 ± √34 , -1)

(-10, -1 ± √34)

Answer 8

as usual, it is C, because it is always C

Answer 9

center is \((-10,-1)\) go \(\sqrt{34}\) units left and right, you get the answer in C

Answer 10

Thank you! But can you answer another question of mines?

Answer 11

What is the eccentricity of the hyperbola given by the equation (y^2/100) - (x^2/36)= 1?