I just want to ask about 3 ANALYTIC GEOMETRY problem...this is our assignment so I really need an answer ASAP?

Question

PROBLEM 1. A square is inscribed in the ellipse whose equation is x squared over 16 plus y squared over 9 equals to 1.. find the coordinates of the vertices of the square; find tehe perimeter and area of the square...

PROBLEM 2. Find the equation of the ellipse with the following data: Distance between directices is equal to 9 times square root of 2 all over 2 and the latus rectum equal to two-thirds.

PROBLEM 3. A parkway 80 ft wide is spanned by a parabolic arc 100 ft long along the horizontal. If the parkway is in the center, how high must the vertex of the arch be in order to give a minimum clearance of 20 ft over teh parkway?


I hope that someone can help me especially the MATH WIZARDS there...please help me.... im really begging you....please...please...please....

I owe you a big thank if you can help me....Thanks!!!

Answer 1

Problem 1 : for the square, at each vertex, we have x = y or x = - y

then x²/16 + x²/9 = 1

25x²/144 = 1

x² = 144/25

the vertices are
(12/5 ; 12/5) (12/5 ; -12/5) (-12/5 ; 12/5)
and (-12/5 ; -12/5)

The perimeter is 4 * 24/5 = 96/5

The area is (24/5)² = 576/25

Answer 2

The questions that get a hundred and forty solutions are in many cases a team of folk attempting to get hassle-free factors. all the solutions are somewhat an identical, and/or do no longer require an excellent form of concept.