The parabola y = x^2 - 2 and ellipse x^2 + 4y^2 = 16 are drawn in the coordinate plane. How many points of intersection do they have?
+128475 y = x^2 - 2 ⇒ x^2 = y + 2 (1)
x^2 + 4y^2 = 16 (2)
Sub (1) into (2) ans we have that
( y + 2) + 4Y2 = 16
4y^2 + y - 14 = 0
(4y - 7) ( y + 2) = 0
Set each factor to 0 and solve for y and we get that
y = 7/4 and y = -2
And y = x^2 - 2 ....so...
7/4 = x^2 - 2 -2 = x^2 - 2
15/4 = x^2 0 = x^2
Take both roots
x = sqrt (15)/2 x = - sqrt (15)/2 and x = 0
So.....we have three points of intersection
Seethe graph here : https://www.desmos.com/calculator/tgmads5grb
