Question

X^2+8x+4y^2-40y+16=0 how do you write this equation in standard form. and identify the related conic?

Answer 1

This is the equation of an ellipse, with center at `(-4,5)` and major axis `20` and minor axis `10`. Standard form is `(x+4)^2/10^2+(y-5)^2/5^2=1`

Explanation:

The given equatiin `x^2+8x+4y^2-40y+16=0` can be written as

`(x^2+8x+16)+4(y^2-10y+25)=100`

or `(x+4)^2/10^2+(y-5)^2/5^2=1`

This is the equation of an ellipse, with center at `(-4,5)` and major axis `20` and minor axis `10`

graph{x^2+8x+4y^2-40y+16=0 [-25, 15, -4.88, 15.12]}