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Algebra ->  Length-and-distance -> SOLUTION: (I hope that I'm putting this in the right category) <img src="http://www.mathamazement.com/images/Pre-Calculus/09_Conic-Sections/09_02_The-Hyperbola/hyperbola-graph-step-1.JPG" /      Log On


   



Question 388591: (I hope that I'm putting this in the right category)

(ignore the numbers)Points(Clock-wise): S(-a, b); P(a, b); Q(a, -b); R(-a, -b)


a. (find missing coordinates. I when ahead and provided all coordinates.)
b. Find the length of the diagonals
c. Describe your results in part (b) as a theorem.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
S(-a, b); P(a, b); Q(a, -b); R(-a, -b)
S(-2,2);P(2,2);Q(2,-2);R(-2,-2)
a. (find missing coordinates. I when ahead and provided all coordinates.)
b. Find the length of the diagonals
S(-2,2);Q(2,-2);
Distance formula
D= sqrt%28%28x1-x2%29%5E2%2B%28y1-y2%29%5E2%29
D= sqrt%28%28-2-2%29%5E2%2B%282-%28-2%29%29%5E2%29
...
D=sqrt%2832%29
...
%28highlight%28D=+5.66%29%29the diagonal length
...
(-2,-2),P(2,2);
Since these pointsform a square the other diagonal will also have same length.
...
m.ananth@hotmail.ca