The orbit of a planet around its star is an ellipse, with the star at one focus. The apoapsis of a planet is its greatest distance from the star, and the periapsis is its shortest distance. Its mean distance is the length of the semimajor axis. The mean distance from a planet to its star is93 million miles. If the apoapsis of the planet is98 million miles, what is the periapsis? Write an equation for the orbit of the planet around the star. The periapsis is million miles.

Solution :

Let the center be (0,0)

Now from the diagram given below ,

The major axis = periapsis + apoapsis

2 x semi major axis = periapsis + 98

2 x 93 = 98 + periapsis

Therefore, periapsis = 186 - 98

                                  = 88 million miles

Star coordinate = (93-98, 0)

                          = (-5,0)

Let the minor axis be 2b

For ellipse

Now, equation of the ellipse

(2,20) means that the 2 is 2 hours and 20 is 20$. so there both 20$ for 2 hours only the same price. like it says. so, the dunk tank and the bounce house are the same price (20$) for the same amount of time (2 hours).

hope i

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.