Question

NEED HELP! Conics - Circles
Write the general conic form equation of each circle.
1. (x + 3)^2 + (y + 6)^2 = 81
2. (x + 6)^2 + (y - 2) = 64
3. (x + 14)^2 + y^2 = 24

Answer 1

Please provide a thorough explanation of how you're doing them. I need to understand this stuff.

Answer 2

hmm

Answer 3

\(\bf (x-{\color{brown}{ h}})^2+(y-{\color{blue}{ k}})^2={\color{purple}{ r}}^2

\qquad center\ ({\color{brown}{ h}},{\color{blue}{ k}})\qquad
radius={\color{purple}{ r}}
\\ \quad \\ \quad \\
hint:\qquad (x {\color{brown}{ +3}})^2 + (y {\color{blue}{ +6}})^2 = {\color{purple}{ 81}}\)

Answer 4

hmmm kinda misread.. the genercal conic hmmm

Answer 5

hint: divide the left side, by the right side

Answer 6

Huh?

Answer 7

\(\bf (x + 3)^2 + (y + 6)^2 = 81 \implies \cfrac{(x + 3)^2}{81} + \cfrac{(y + 6)^2}{81} = \cfrac{\cancel{81}}{\cancel{81}}
\\ \quad \\
\textit{keeping in mind }
\\ \quad \\
\cfrac{(x-{\color{brown}{ h}})^2}{{\color{purple}{ a}}^2}+\cfrac{(y-{\color{blue}{ k}})^2}{{\color{purple}{ b}}^2}=1

\qquad center\ ({\color{brown}{ h}},{\color{blue}{ k}})\qquad
vertices\ ({\color{brown}{ h}}\pm a, {\color{blue}{ k}})
\)

Answer 8

also keep in mind that +3 = - (-3)

Answer 9

@jdoe0001 I think they want to expand everything out?

For example, (x + 3)^2 = x^2 + 6x + 9

Answer 10

Now what?

Answer 11

Dat sit!! They ask you to get the conic form, just divide both side by the right hand side and you get the conic form of a circle.

Answer 12

I'm not getting it. o.o

Answer 13

To get more details, you can say that that is the "ellipse" with vertices are (\(0,\pm 9\) ) and (\(\pm9, 0)\) Foci (0,0)

Answer 14

@jim_thompson5910 hmmm methinks is the conic version of it, rather than an expanded one

Answer 15

Why not?
Like parabola, you have 2 different forms: Standard form and vertex form.
Same as circle.

Answer 16

@jdoe0001 you are invisible to me again. :)

Answer 17

hmmm odd

Answer 18

anyhow @Teddyiswatshecallsme there, make it like an ellipse equation
keep in mind that +3 = -(-3) and that +6 = -(-6)

Answer 19

Sorry, parabola has 3 forms, polar form also. :)