Question

How do you graph the conic `16x^2-24xy+9y^2-60x-80y+100=0` by first rotations the axis and eliminating the xy term?

Answer 1

The axis: Parallel to 4x-3y=0, The tangent at the vertex:parallel to 3x+4y-10=0. The graph is inserted for direct view on which is which.

Explanation:

The second degree terms form a perfect square. So, the conic is a

parabola.

When reorganized to the standard form,

`(4x-3y)^2-20(3x+4y-10)=0`

This form reveals that

The axis: Parallel to 4x-3y=0,

The tangent at the vertex:parallel to 3x+4y-10=0.

I expect in other answers the rotation method.

graph{(4x-3y)^2-20(3x+4y-10)=0 [-20, 20, -10, 10]}