Question

Complete the standard form of the equation of the ellipse represented by the equation  9x2 + 4y2 − 36x +

Answer 1

We start with writing the terms containing x and y together. We get 9x^2 + 36x + 4y^2 – 8y + 4 =0

=> 9(x^2 + 4x) + 4(y^2 – 2y) + 4 =0

Now complete the squares

=> 9(x^2 + 4x +4) +4(y^2 – 2y +1) = -4 + 36 + 4

divide both the sides by 36

=> (x^2 + 4x +4)/4 + (y^2 – 2y +1)/9 = 1

=> (x + 2)...

Answer 2

`((x-2)^(2))/(4) + (y^(2))/(9) = 1`

Explanation:

The standard form of the ellipse is determined by completing the squares and some algebraic handling:

`(3\cdot x)^(2) - 12\cdot(3\cdot x) + 36 +4\cdot y ^(2) - 36 = 0`

`(3\cdot x - 6)^(2) + 4\cdot y^(2) = 36`

`9\cdot (x -2)^(2) + 4\cdot y^(2) = 36`

`((x-2)^(2))/(4) + (y^(2))/(9) = 1`