SOLUTION: Locate the points of intersection of the parabola x^2+y=5 and ellipse 4x^2 +y^2 = 17.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Locate the points of intersection of the parabola x^2+y=5 and ellipse 4x^2 +y^2 = 17.      Log On


   

Question 904323: Locate the points of intersection of the parabola x^2+y=5 and ellipse 4x^2 +y^2 = 17.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Do you want to solve for y and substitute into the ellipse equation, or do you want to solve for x and substitute into the ellipse equation?

x%5E2%2By=5
x%5E2=5-y
Substitute x%5E2.

4x%5E2%2By%5E2=17
4%285-y%29%2By%5E2=17
20-4y%2By%5E2-17=0
y%5E2-4y%2B3=0
%28y-1%29%28y-3%29=0

If y=1, then x%5E2=5-1
x%5E2=4
x=-2 or x=2.
Solution Points For This: (-2,1) and (2,1).

If y=3, then x%5E2=5-3=2
x=-sqrt%282%29 or x=sqrt%282%29.
Solution points for this are: (-sqrt(2),3) and (sqrt(2),3).