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anonymous
 one year ago
Can someone help me with my conic sections assignment? I'm really confused.
anonymous
 one year ago
Can someone help me with my conic sections assignment? I'm really confused.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I have a few that I really don't know how to do, but here's one: What is the equation of the following graph?

phi
 one year ago
Best ResponseYou've already chosen the best response.3First, what shape is that? is it a circle, ellipse, parabola or hyperbola?

phi
 one year ago
Best ResponseYou've already chosen the best response.3next, look in your notes for the equation of an ellipse. can you write down the "general form" ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ x^{2} }{ a ^{2}} + \frac{ y ^{2}}{ b ^{2} }\]

phi
 one year ago
Best ResponseYou've already chosen the best response.3an equation has an = sign in it. it should be \[ \frac{ x^{2} }{ a ^{2}} + \frac{ y ^{2}}{ b ^{2} }=1 \] but that is for an ellipse whose center is at (0,0) your ellipse is not centered at (0,0). The better equation is \[ \frac{ (xh)^{2} }{ a ^{2}} + \frac{ (yk) ^{2}}{ b ^{2} } =1\] where (h,k) is the center of the ellipse. Can you figure out what point is in the exact center of your ellipse ?

phi
 one year ago
Best ResponseYou've already chosen the best response.3that means you know (h,k) h=0 and k= 2 put those into the equation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{(x0)^{2} }{ a ^{2} }+ \frac{ (y+2)^{2} }{ b ^{2}}\]

phi
 one year ago
Best ResponseYou've already chosen the best response.3= 1 don't leave that out also, x0 simplifies to x so \[ \frac{x^{2} }{ a ^{2} }+ \frac{ (y+2)^{2} }{ b ^{2}} =1 \]

phi
 one year ago
Best ResponseYou've already chosen the best response.3now for the "a" value: that is the distance in the xdirection (sideways) from the center to the side. what is the value of "a" ?

phi
 one year ago
Best ResponseYou've already chosen the best response.3yes, a is 1 and a^2 which means a*a is 1*1 = 1 so \[ \frac{x^{2} }{ a ^{2} }+ \frac{ (y+2)^{2} }{ b ^{2}} =1 \\ \frac{x^{2} }{ 1 ^{2} }+ \frac{ (y+2)^{2} }{ b ^{2}} =1 \] now find b, which the distance from the center to the top (i.e. in the up/down direction , or yaxis direction)

phi
 one year ago
Best ResponseYou've already chosen the best response.3\[ \frac{x^{2} }{ 1 ^{2} }+ \frac{ (y+2)^{2} }{ 3^{2}} =1 \] we could simplify that a little, and write \[ x^2 + \frac{ (y+2)^{2} }{ 9} =1 \] but either way is ok

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So is that the final answer?

phi
 one year ago
Best ResponseYou've already chosen the best response.3yes. You can check some points to make sure it's correct. for example , when x is 0 you get \[ 0^2 + \frac{ (y+2)^{2} }{ 9} =1 \\ \frac{ (y+2)^{2} }{ 9} =1 \\ (y+2)^2= 9 \\ y+2= \pm 3 \] and y= +32= 1 or y= 32= 5 so points (0,1) and (0, 5) should be on the ellipse.
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