Question

What type of conic is represented by `9x^2+16y^2+18x+64y-71=0`?

Answer 1

The equation represents the ellipse with center at `(-1, -2)`, axes parallel to the axes of coordinates and semi axes 4 and 3...

Explanation:

In the absence of xy-term, the equation can be reorganized as

`(9(x+1)^2-9)+(16(y+2)^2-64)-71=0`.

In the standard form, this is

`(x+1)^2/4^2+(y+2)^2/3^2=1`
.
Now, the equation represents the ellipse with center at `(-1, -2)`,

axes parallel to the axes of coordinates and semi axes 4 and 3...