A planet follows an elliptical path described by 81x^2+9y^2=729. A comet follows the parabolic path y=x^2-9. Where might the comet intersect the orbiting planet?

Answer 1

At 3 points, (0-9), (3,0) and (-3,0)

x^2/3^2 + y^2/9^2 = 1 is an ellipse with y intercepts (0,-9) and (0,9)

y=x^2 -9 has y intercept (0,-9)

the ellipse also intersects the parabola at its x intercepts, (3,0) and (-3,0)