Question

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

Answer 1

Hyperbola

Explanation:

`a,b \\eq 0`

`((x-h)^2)/(a^2)+((y-k)^2)/(b^2)=1` is an ellipse.

`((x-h)^2)/(a^2)-((y-k)^2)/(b^2)=1` is a hyperbola.

`((y-k)^2)/(b^2)-((x-h)^2)/(a^2)=1` is also a hyperbola.

`((x-h)^2)/(a^2)+((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).