The planets move around the sun in elliptical orbits with the sun at one focus. the point in the orbit at which the planet is closest to the sun is called perihelion, and the point at which it is farthest is called aphelion. these points are the vertices of the orbit. a planet's distance from the sun is 741,000,000 km at perihelion and 817,000,000 km at aphelion. find an equation for the planet's orbit. (place the origin at the center of the orbit with the sun on the x-axis. use the following as necessary: x, y.)

Consider the attached ellipse. Let the sun be at the right focus. Then perihelion is at right vertex on the x-axis and aphelion is at the left vertex on the x-axis.

The distances:

Then

Add these two equations:

and subtract first equation from the second:

Note that thus

The equation for the planet's orbit is

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation:

answer: a

step-by-step explanation: the answer is a due to the rule of symmetry; that a line of symmetry must divide a figure into 2 pieces that are the exact same, only reflected over a line of symmetry. b and c do not have lines of symmetry and would not divide the figure evenly, thus making the answer a.