Problem solving with algebra and linear equations help!!

Question

The linear path of a comet is x-2y=4. The orbit of a planet around a star is represented by the equation x²+y²=25. The planet orbits the star at a distance of 450 million kilometres. The star is located at point (0,0). A satellite orbiting the star is represented by the equation 3x²+10y²=150. The comet, planet and satellite all orbit the sun in the same plane. At what distances from the star will the comet intersect with the orbit of the planet and satellite?

Answer 1

just some rough rounded off calculations

but the planet and comet come together at about (-3.4, -3.7)

the planet and satelite come together at about (-2.8, -3.4)

those two points are less than 0.7 apart

maybe half way or (-3.1, -3.5) is where all 3 come closest together.

the comet's path is a slightly upward sloping straight line

the planet's path is a circle, center at the origin, radius =5

the satelite's path is an ellipse, with minor axis about 8 and major axis about 14

about (-3.1,-3.5) is within about 0.3 from where the planet, comet and satelite come closest to intersecting.