Question

How do I graph `16x^2-9y^2+32x+18y-137=0` algebraically?

Answer 1

Ellipse centered at (-1,1) and semi major axis of 4 unitsalong y axisand semi minor axis of 3 units.

Explanation:

Write the equation in standard form by completing the squares,

`16x^2 +32x -9y^2 +18y -137=0`

`16(x^2 +2x +1) -9(y^2 -2y +1) -16 +9-137=0`

`16(x+1)^2 -9(y-1)^2=144`

`(x+1)^2 /3^2 - (y-1)^2 /4^2 =1`

This is an ellipse with its centre at (-1,1), with semi-major axis of 4 units along y axis and semi-minor axis of 3 units along x axis