Question

Classify each conic section, write its equation in standard form.

x^2+y^2+8y+15=0

And

-2y^2+x-20y-45=0

Answer 1

Ax^2+Bxy+Cy^2+Dx+Ey+F=0


if A=C you most likely have a circle (you know if your r is real)
if A or C (not both) is 0 then you have a parabola
if A and C differ in sign you have a hyperbola
if A and C have same sign (but you know different number) you have an ellipse

Answer 2

If B2 - 4AC is... then the curve is a...
< 0 ellipse, circle, point or no curve.
= 0 parabola, 2 parallel lines, 1 line or no curve.
> 0 hyperbola or 2 intersecting lines.

Answer 3

I thought those were the rules?

Answer 4

and I should have put on my if the conic exists

Answer 5

yes I see those also used before

Answer 6

Ax^2+Bxy+Cy^2+Dx+Ey+F=0 << that seems like the general equation.

Answer 7

where A, B, C, D, E and F are constants.

Answer 8

yep that is the general equation for any conic

Answer 9

According to wolfram it classifies it as a circle.

Answer 10

But I noticed that x^2 is just (x)^2 and y^2 +8y+15 is just (y+5)(y+3) factored
so x^2 + (y+5)(y+3).