Where might the comet intersect the orbiting​ planet?

Question

A planet follows an elliptical path described by 256x2+16y2=4096.  

A comet follows the parabolic path y=x2−16.  

Where might the comet intersect the orbiting​ planet?

Answer 1

256x² + 16y² = 4096

16x² + y² = 256

x² = y + 16

16(y + 16) + 16y² = 256

16y + 256 + 16y² = 256

16y + 16y² = 256

y + y² = 16

y² + y = 16

y² + y + 1/4 = 16 + 1/4

(y + 1/2)² = 65/4

y + 1/2 = ±√65 / 2

y = (-1 ±√65) / 2