2 word problems on ellispes

[Guest]

I need help on these questions. They're similar. A lot of reading..and they both confuse me.

Johannes Kelper was a physicist who devised the three laws of planetary motion. Kepler's First Law states that all planets orbit the sun in elliptical paths, with the centre of the sun at one focus. The distance from the sun to a planet continually changes. The Earth is closest to the sun in January. The closest point or perihelion, is 1.47*10^8 km from the sun. The Earth is farthest from the sun in July. The farthest point, or aphelion, is 1.52*10^8 km from the sun. Write an equation of the ellipse that models the Earth's orbit about the sun. Assume that the centre of the ellipse is at the orgin and that the major axis is along the x-axis


SO I drew the picture, I was able to do that, but I don't get hor you find the equation. How do you find where the Sun is at knowing the distances?? If it helps, the equation is suppose to be x^2/2 235 025 * 10^10 + y^2/2 234 400*10^10=1

2nd question: Halley's Comet orbits the sun every 76 years. The comet travels in an elliptical path, with the sun at one of the foci. At the closest point, or perihelion, the distance of the comet to the sun is 8.8*10^7km. At the furthest point, or aphelion, the distance of the comet from the sun is 5.3*10^9 km. Write an equation of the ellipse that models the path of Halley's Comet. Assume the sun is on the x-axis.

I tihnk tihs question is similar to the previour question I posed. The answer for this question is x^2/702570636*10^12 +y^2/466 410 *10^12=1

I Don't get how to find out the answer, help plz..
-Anna

 

[Gene]

The equation is x^2/a^2+y^2/b^2 = 1
When you drew the picture you should have had the major axis = 1.49 + 1.52
{I'm hiding the * 10^8 till the end.}
The semi-major axis (a) is 1/2 of that or 1.495 and the foci are at +.025
The semi-minor axis is the height of the triangle formed by the y axis, the .025 leg and the 1.495 hypot (the semi-major axis).
b=sqrt(a^2-.025^2)
{bring back the * 10^8 now.}
Plug a & b into the equation.

You are correct, the second is the same as this one.