Question

Explain your process for writing the standard form equation for an ellipse.

Answer 1

From what? Given information or general form?

Answer 2

I have no idea, that's all that it says :(

Answer 3

That's why I'm here haha

Answer 4

Well, have you learned the form ax^2 + by^2 + cx + dy + f = 1 yet?

Answer 5

Yes

Answer 6

I'll just explain that then.

Answer 7

well it's e, but you know that :P

Answer 8

Wait isnt that a hyperbola?:O not an ellipse?

Answer 9

An ellipse is added in between.

Answer 10

First predict what type of conic it is. If the squared terms are both positive, but different coefficients, then it's an ellipse. Let's use the example:
4x^2 + 9y^2 - 32x + 36y + 64 = 0
4x^2 + 9y^2 - 32x + 36y = -64
Then, rewrite the conic so that the x and the y together.
4x^2 - 32x + 9y^2 + 36y = -64
Factor out a 4 from the x terms.
4(x^2 - 8x) + 9y^2 + 36y = -64
Factor out a 9 from the y terms.
4(x^2 - 8x) + 9(y^2 + 4y) = -64
Complete the square for both the x and y terms and balance the equation by adding to both sides.
4(x^2 - 8x + 16) + 9(y^2 + 4y + 4) = -64 + 64 + 36
Add like terms.
4(x^2 - 8x + 16) + 9(y^2 + 4y + 4) = 36
Factor the perfect squares.
4(x - 4)^2 + 9(y + 2)^2 = 36
Divide both sides by 36.
(x - 4)^2/9 + (y + 2)^2/4 = 1

Answer 11

Thank you so much!

Answer 12

You're welcome.