Question

Identify the conic given by (x-8)^2/64 - (y-9)^2/4. = 1

Answer 1

Answer:

Hyperbola

Step-by-step explanation:

$a,b \neq 0$

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$ is an ellipse.

$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$ is a hyperbola.

$\frac{(y-k)^2}{b^2}-\frac{(x-h)^2}{a^2}=1$ is also a hyperbola.

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$ is a circle if $a^2=b^2$.

Notice the signs between each squared term.

It was the same sign for ellipse and circle (no minus; only plus).

It was different for hyperbola (+ to - for both).