SOLUTION: A rectangle inscribed in the circle x^2 + y^2 = 25 on the coordinate grid has an area of 48 square units. What are the coordinates of the vertices of the rectangle? Picture of c

Algebra ->  Coordinate-system -> SOLUTION: A rectangle inscribed in the circle x^2 + y^2 = 25 on the coordinate grid has an area of 48 square units. What are the coordinates of the vertices of the rectangle? Picture of c      Log On


   



Question 965432: A rectangle inscribed in the circle x^2 + y^2 = 25 on the coordinate grid has an area of 48 square units. What are the coordinates of the vertices of the rectangle?
Picture of circle posted below
http://postimg.org/image/k1znbxle3/
Thank you so much!! ☺

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This is only a start, not a finished solution:

Imagine a point in quadrant one, (p,s) on the circle.
The three other points for the rectangle are (-p,s), (p,-s), and (-p,-s). Area of this rectangle would be 2s%2A2p=48.

Your circle containing those four corners of the rectangle is radius 5,
p%5E2%2Bs%5E2=25.

Those seem to be two equations in two variables. No real need to pick the new variables p and s, so just go back to x and y, since they still are variables.

system%28xy=48%2F4%2Cx%5E2%2By%5E2=25%29

system%28xy=12%2Cx%5E2%2By%5E2=25%29

y=12%2Fx
-
x%5E2%2B%2812%2Fx%29%5E2=25

.....you should continue...............