Question

How do you graph `4x^2+4y^2+24x+32y+75=0`?

Answer 1

Draw a circle with center at `(-3,-4)` and a radius of `2 1/2` units.

Explanation:

`4x^2+4y^2+24x+32y+75=0`

`rarr 4(x^2+6xcolor(white)("XXX"))+4(y^2+8ycolor(white)("XXX"))=-75`

`rarr 4(x^2+6x+3^2)+4(y^2+8y+4^2) = -75+ 4 * (3^2) + 4 * (4^2)`

`rarr 4(x+3)^2+4(y+4)^2 = 25`

`rarr (x+3)^2+(y+4)^2=25/4 = (5/2)^2`

which is the standard form for a circle with center `(-3,-4)` and radius `5/2=2 1/2`

graph{4x^2+4y^2+24x+32y+75=0 [-7.61, 4.88, -6.81, -0.566]}