Teddyiswatshecallsme
  • Teddyiswatshecallsme
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
Mathematics
chestercat
  • chestercat
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Teddyiswatshecallsme
  • Teddyiswatshecallsme
Please provide a thorough explanation of how you're doing them. I need to understand this stuff.
hwyl
  • hwyl
hmm
jdoe0001
  • jdoe0001
\(\bf (x-{\color{brown}{ h}})^2+(y-{\color{blue}{ k}})^2={\color{purple}{ r}}^2 \qquad center\ ({\color{brown}{ h}},{\color{blue}{ k}})\qquad radius={\color{purple}{ r}} \\ \quad \\ \quad \\ hint:\qquad (x {\color{brown}{ +3}})^2 + (y {\color{blue}{ +6}})^2 = {\color{purple}{ 81}}\)

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jdoe0001
  • jdoe0001
hmmm kinda misread.. the genercal conic hmmm
jdoe0001
  • jdoe0001
hint: divide the left side, by the right side
Teddyiswatshecallsme
  • Teddyiswatshecallsme
Huh?
jdoe0001
  • jdoe0001
\(\bf (x + 3)^2 + (y + 6)^2 = 81 \implies \cfrac{(x + 3)^2}{81} + \cfrac{(y + 6)^2}{81} = \cfrac{\cancel{81}}{\cancel{81}} \\ \quad \\ \textit{keeping in mind } \\ \quad \\ \cfrac{(x-{\color{brown}{ h}})^2}{{\color{purple}{ a}}^2}+\cfrac{(y-{\color{blue}{ k}})^2}{{\color{purple}{ b}}^2}=1 \qquad center\ ({\color{brown}{ h}},{\color{blue}{ k}})\qquad vertices\ ({\color{brown}{ h}}\pm a, {\color{blue}{ k}}) \)
jdoe0001
  • jdoe0001
also keep in mind that +3 = - (-3)
jim_thompson5910
  • jim_thompson5910
@jdoe0001 I think they want to expand everything out? For example, (x + 3)^2 = x^2 + 6x + 9
Teddyiswatshecallsme
  • Teddyiswatshecallsme
Now what?
anonymous
  • 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.
Teddyiswatshecallsme
  • Teddyiswatshecallsme
I'm not getting it. o.o
anonymous
  • 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)
jdoe0001
  • jdoe0001
@jim_thompson5910 hmmm methinks is the conic version of it, rather than an expanded one
anonymous
  • anonymous
Why not? Like parabola, you have 2 different forms: Standard form and vertex form. Same as circle.
anonymous
  • anonymous
@jdoe0001 you are invisible to me again. :)
jdoe0001
  • jdoe0001
hmmm odd
jdoe0001
  • jdoe0001
anyhow @Teddyiswatshecallsme there, make it like an ellipse equation keep in mind that +3 = -(-3) and that +6 = -(-6)
anonymous
  • anonymous
Sorry, parabola has 3 forms, polar form also. :)

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