Another circles intercepts question

[JackSonSmith]

Find the coordinates of the points of intersection of the curves

x^2 / 4  + y^2 / 9  = 1   and  x^2 / 9  +  y^2 / 4  = 1

[Tyleralp1]

Transpose each side for y:

y=sqrt(9-(9x^2)/4)
y=sqrt(4-(4x^2)/9)

Let the sides equal each other and square both sides:
9-(9x^2)/4 = 4-(4x^2)/9

Solve for x.

Sub answer back into equation, to find the respective y coordinate.

[Phy124]

Handy knowledge - If you have two ellipses of the form and , the points of interception of the two are given by .

How was this derived you might question? Simply put, one ellipse is the other flipped about the line (or similarly ) so we know they will intercept somewhere along these lines. Take one of the equations and sub in for , I'll use the first one. We have . We know the solutions are along the lines so the solutions for are the same and you now have your four points. Yay for killing time waiting to check out boxing day sales by doing maths

[keltingmeith]

Yay for killing time waiting to check out boxing day sales by doing maths

Then doing more maths because they didn't calculate the new price for you, they just told you the discount.

[lzxnl]

Transpose each side for y:

y=sqrt(9-(9x^2)/4)
y=sqrt(4-(4x^2)/9)

Let the sides equal each other and square both sides:
9-(9x^2)/4 = 4-(4x^2)/9

Solve for x.

Sub answer back into equation, to find the respective y coordinate.

I'd solve for y^2 instead and set them equal to each other.