How do you identity if the equation 5x2+6x4y=x2y22x is a parabola, circle, ellipse, or hyperbola and how do you graph it?

1 Answer
Dec 1, 2016

This is an ellipse (x+1)2(2)2+(y2)2(8)2=1

Explanation:

Let's rearrange the equation

5x2x2+6x+2x+y24y=0

4x2+8x+y24y=0

Completing the squares

4(x2+2x+1)+(y24y+4)=8

4(x+1)2+(y2)2=8

Dividing by 8

(x+1)22+(y2)28=1

(x+1)2(2)2+(y2)2(8)2=1

This is the equation of an ellipse

(xh)2a2+(yk)2b2=1

The center is (1,2)

c=b2a2=6

The foci are F(1,2+6) and F'(1,26)

The major axis is =26

The minor axis is =22

graph{4x^2+8x+y^2-4y=0 [-6.99, 7.06, -1.27, 5.754]}