Equation of ellipse in the first two quadrants

[cherica123]

Write the equation of the part of the graph of an ellipse

x^2/a^2 + y^2/b^2 =1


all ive done is try to play around with rearranging the equation....but i dont know what im looking for so it was just taking random paths. Help please! Thank you!

 

[mark07]

The equation gives the full ellipse.

Which part of the graph do you need an equation for?

As you typed, question is obviously missing information...

EDIT: I should start reading the subject lines... Sorry about that.

 

[cherica123]

oh wow im sorry, i completely forgot the important part for the problem! It has to be found for just the first two quadrants. Sorry about that!

 

[soroban]

Hello, cherica123!

I think I understand what you're looking for.
You hid part of the problem in the heading.

Write the equation of the part of the graph of an ellipse
. . \(\displaystyle \L\frac{x^2}{a^2}\,+\,\frac{y^2}{b^2}\;=\;1\)

They gave us the equation for the entire ellipse.
We are to write the equation of the semiellipse in quadrants 1 and 2.

We are given: \(\displaystyle \L\:\frac{x^2}{a^2} \,+\,\frac{y^2}{b^2}\:=\:1\)


\(\displaystyle \text{Solve for }y\text{ . . . Multiply through by }a^2b^2\)

. . \(\displaystyle \L b^2x^2\,+\,a^2y^2\;=\;a^2b^2\)

. . . . . . . . . \(\displaystyle \L a^2y^2\;=\;a^2b^2\,-\,b^2x^2 \:=\:b^2(a^2\,-\,x^2)\)

. . . . . . . . . . . \(\displaystyle \L y^2\;=\;\frac{b^2}{a^2}(a^2\,-\,x^2)\)

. . . . . . . . . . . .\(\displaystyle \L y\;=\;\pm\frac{b}{a}\sqrt{a^2\,-\,x^2}\)


Since we want only the upper half of the ellipse,

. . the equation is: \(\displaystyle \L\:y\:=\:\frac{b}{a}\sqrt{a^2\,-\,x^2}\)