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anonymous
 one year ago
What is the equation of the following graph?
anonymous
 one year ago
What is the equation of the following graph?

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UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1looks like an ellipse, where is it centred? what are the semimajor axes?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it is, and isn't it centered at (0,0)? and I don't know them..

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1yes it is centred at the origin: (0,0)

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1Semi major axes of an ellipse look like this dw:1439092799738:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439092817312:dw we have to use this equation, correct?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1A general form of an ellipse centred at the point \((h,k)\), with semi major axes \(a\), and \(b\), (in the x and y directions respectively ) is \[\frac{(xh)^2}{a^2}+\frac{(yk)^2}{b^2} = 1\]

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1yeah we have the centre \((h,k)\) = \((0,0)\) so it reduces to \[\frac{x^2}{a^2}+\frac{y^2}{b^2} = 1\]

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1we just need to get \(a\), (half the width) and \(b\), (half the height)

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1look at the diagram,

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1dw:1439093170591:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so then A would be 1.5, and B would be 3 ?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1not quite, the full width of the ellipse is 3  (3) = 6 the full height of the ellipse is 6  (6) = 12 so half the width is 6/2 = ... and the half height is 12/2 = ......

anonymous
 one year ago
Best ResponseYou've already chosen the best response.03, and 6, or is it in that fraction form?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1thats right the semimajor axis (in the x direction) : a = 3 and the semimajor axis in the y direction: b = 6

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1So what does the equation of our ellipse look like now?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439093577574:dw

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1goood, now just simplify 3^2 and simplify 6^2

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1Cool, so your equation is \[\frac{x^2}9+\frac{y^2}{36} = 1\] A further step to make the final equation a little nicer could be to multiply both sides by 9 \[x^2+\frac{y^2}{4} = 9\] but you might prefer to keep it as \(\frac{x^2}9+\frac{y^2}{36} = 1\)

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1i suppose another option for a nice final form might be \[\left(\frac x3\right)^2+\left(\frac y6\right)^2=1\] They all kinda look nice.
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