SOLUTION: I need help to solve a equation in ellipse form. What is the X-variable equal to? {{{ x^2/525^2 + y^2/350^2 = 1}}}

Algebra ->  Algebra  -> Quadratic-relations-and-conic-sections -> SOLUTION: I need help to solve a equation in ellipse form. What is the X-variable equal to? {{{ x^2/525^2 + y^2/350^2 = 1}}}      Log On

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Question 117842: I need help to solve a equation in ellipse form. What is the X-variable equal to? +x%5E2%2F525%5E2+%2B+y%5E2%2F350%5E2+=+1
Answer by MathLover1(3376) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
The equation of an ellipse (with horizontal major axis) in standard form: %28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2=1
x%5E2%2F525%5E2+%2B+y%5E2%2F350%5E2=1

From given equation, we can say that this is an ellipse with a+=+526 and b+=+350 (note: a+%3Eb), and has the center in the origin (0,0) since the h=0 and k=0

1+-+x%5E2%2F525%5E2+=+y%5E2%2F350%5E2…………..multiply both sides by 350%5E2
%28-x%5E2%2F525%5E2%29+350%5E2%2B+%281%2A350%5E2%29+=+y

-%28x+%5E2%29%28350%5E2%2F525%5E2%29+%2B+350%5E2=y……………………………………………

Since 350%5E2%2F525%5E2=350%2A350%2F%28525%2A525%29=%28350%3A175%29%28350%3A175%29%2F%28%28525%3A175%29%28525%3A175%29%29=+2%2A2%2F%283%2A3%29=4%2F9, we have

-x%5E2+%284%2F9%29+%2B+350%5E2=y……………

Set y+=+0 in the equation obtained and find the+x+%96intercepts.

-x%5E2+%284%2F9%29+%2B+350%5E2=+0+……………move -x%5E2+%284%2F9%29 to the right

350%5E2+=+x%5E2+%284%2F9%29………divide both sides by 4%2F9

350%5E2%2F%284%2F9%29+=+x%5E2+%2A%284%2F9%29%2F%28+4%2F9%29………

9%2A350%5E2%2F4=+x%5E2+………

9%2A122500%2F4=+x%5E2+………

9%2A30625=+x%5E2+………

275625=+x%5E2+………

x%5B1%2C2%5D+=+sqrt+%28275625%29%29………..
So,
x%5B1%5D+=+525
x%5B2%5D+=+-525