Question 872566
X^2 +y^2=25 intersects the curve 2x^2-3y^2=5

X^2 +y^2=25.......(1) 
2x^2-3y^2=5........(2)

multiply eq. (1) by 3 and add to (2)
3x^2+3y^2=75
2x^2-3y^2=5

5x^2=80
x^2=16

x= +/- 4

Plug x=+/- 4 in eq(1)

y^2+16=25
y^2=9
y=+/-3

The points of intersection are

(4,3),(4,-3),(-4,3)(-4,-3)