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# Coordinate Systems [P5] watch

1. hmmm maths seems to be getting hard.

Ok im stuck on this question.
Prove that the ellipse 4x^2 + 9y^2 = 36 and the hyperbola 4x^2 - y^2 = 4 have the same foci.
Sketch the two curves on the same diagram.
Find the intersections of the 2 curves, and show that they intersect at right angles in the first quadrant. ?

Ok basically i found a and b for both. put them into the excentricity formulae and i dont get the same foci :s
2. (Original post by Syncman)
hmmm maths seems to be getting hard.

Ok im stuck on this question.
Prove that the ellipse 4x^2 + 9y^2 = 36 and the hyperbola 4x^2 - y^2 = 4 have the same foci.
Sketch the two curves on the same diagram.
Find the intersections of the 2 curves, and show that they intersect at right angles in the first quadrant. ?

Ok basically i found a and b for both. put them into the excentricity formulae and i dont get the same foci :s
Ellipse becomes x^2/9 + y^2/4 = 1.

So a = 3, b = 2 and e = rt(1-b^2/a^2) = rt(5)/3.

Focus at (ae,0) = (rt(5),0).

Hyperbola becomes x^2-y^2/4 = 1

So a = 1, b = 2 and e = rt(1+b^2/a^2) = rt(5)

Focus at (ae,0) = (rt(5),0)
3. ah id forgotted to square b for the hyperbollic eqn thingy. LoL i swear its not gonna be my knowlage that fails me.... Its gonna be my basic algebra!
4. Prove that the ellipse 4x^2 + 9y^2 = 36 and the hyperbola 4x^2 - y^2 = 4 have the same foci.
Use the standard result for positions of the foci.

Sketch the two curves on the same diagram.
Find where the foci and directrices are first do the curve.

Find the intersections of the 2 curves, and show that they intersect at right angles in the first quadrant. ?
Find the point at which they intersect by equating the expressions for 4x^2 in the two curves. Differentiate to find the gradient of each curve at the point of intersection. If the product of these gradients is equal to -1 then they intersect at right angles.

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