## Teddyiswatshecallsme one year ago 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

1. Teddyiswatshecallsme

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

2. anonymous

hmm

3. anonymous

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

4. anonymous

hmmm kinda misread.. the genercal conic hmmm

5. anonymous

hint: divide the left side, by the right side

6. Teddyiswatshecallsme

Huh?

7. anonymous

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

8. anonymous

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

9. jim_thompson5910

@jdoe0001 I think they want to expand everything out? For example, (x + 3)^2 = x^2 + 6x + 9

10. Teddyiswatshecallsme

Now what?

11. anonymous

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.

12. Teddyiswatshecallsme

I'm not getting it. o.o

13. anonymous

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

14. anonymous

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

15. anonymous

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

16. anonymous

@jdoe0001 you are invisible to me again. :)

17. anonymous

hmmm odd

18. anonymous

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

19. anonymous

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