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

Sep 26, 2015

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,

$16 {x}^{2} + 32 x - 9 {y}^{2} + 18 y - 137 = 0$

$16 \left({x}^{2} + 2 x + 1\right) - 9 \left({y}^{2} - 2 y + 1\right) - 16 + 9 - 137 = 0$

$16 {\left(x + 1\right)}^{2} - 9 {\left(y - 1\right)}^{2} = 144$

${\left(x + 1\right)}^{2} / {3}^{2} - {\left(y - 1\right)}^{2} / {4}^{2} = 1$

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