Replace the polar equation with equivalent Cartesian equations. \frac{x^{2}}{9}+\frac{y^{2}}{4}=1

Mylo O'Moore

Mylo O'Moore

Answered question

2021-06-07

Replace the polar equation with equivalent Cartesian equations. x29+y24=1

Answer & Explanation

svartmaleJ

svartmaleJ

Skilled2021-06-08Added 92 answers

Step 1
We have given a cartesian equation x29+y24=1. The equation x29+y24=1 is a standard form of ellipse
x2a2+y2b2=1 and generally, we take polar coordinates x as a cos0.
Here, a=3. So set x=3cos0. Now, substitute x=3cos0 in x29+y24=1
(3cos0)29+y24=1
9cos209+y24=1
Step 2
Use the identity 1cos20=sin20 to simplify it further.
cos20+y24=1
y24=1cos20
=sin20
y2=4sin20
Take square root on both sides to find y. Consider only positive sign.
y2=±4sin20
y=±2sin0
y=2sin0 [Take only (+) sign]
Hence, the polar equation is x=3cos0,y=2sin0.
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-24Added 2605 answers

Answer is given below (on video)

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