Solve the equation for an ellipse for y. Assume that y > 0. y^2/a^2 + x^2/b^2 = 1
Question
2 Answer

1. User Answers Anonym
multiply each term by a^2b^2:
b^2y^2 + a^2x^2 = a^2b^2
subtract a^2x^2 from both sides
b^2y^2 = a^2b^2  a^2x^2
Now divide both sides by b^2
y^2 = a^2  a^2x^2 / b^2 = a^2 (1  x^2/b^2)
take positive square root ( because y > 0)
y = a sqrt(1  x^2/b^2) 
2. User Answers virtuematane
Answer:
The required value of y is:
[tex]y=a\sqrt{1\dfrac{x^2}{b^2}}[/tex]
Stepbystep explanation:
We have to solve the equation for an ellipse for y.
That means we have to find the value of y in terms of x from the given equation.
The equation of an ellipse is given as:
[tex]\dfrac{y^2}{a^2}+\dfrac{x^2}{b^2}=1[/tex]
We will multiply both side by [tex]a^2b^2[/tex] to obtain:
[tex]b^2y^2+a^2x^2=a^2b^2[/tex]
Now we will take the term of variable 'x' to the right hand side to obtain:
[tex]b^2y^2=a^2b^2a^2x^2\\\\y^2=\dfrac{a^2b^2a^2x^2}{b^2}\\\\y^2=\dfrac{a^2b^2}{b^2}\dfrac{a^2x^2}{b^2}\\\\y^2=a^2\dfrac{a^2x^2}{b^2}\\\\y^2=a^2(1\dfrac{x^2}{b^2})[/tex]
No on taking square root on both the side we obtain:
[tex]y=a\sqrt{1\dfrac{x^2}{b^2}}[/tex]
Hence, the required value of y is:
[tex]y=a\sqrt{1\dfrac{x^2}{b^2}}[/tex]