Question

Convert to standard form 25x^2 + 4y^2 - 50x -75 = 0

Answer 1

`((x-1)^(2))/(4)+(y^(2))/(25)=1`

Explanation:

we have

`25x^(2)+4y^(2)-50x-75=0`

Convert to standard form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`(25x^(2)-50x)+4y^(2)=75`

Factor the leading coefficient of each expression

`25(x^(2)-2x)+4y^(2)=75`

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

`25(x^(2)-2x+1)+4y^(2)=75+25`

`25(x^(2)-2x+1)+4y^(2)=100`

Rewrite as perfect squares

`25(x-1)^(2)+4y^(2)=100`

Divide both sides by the constant term to place the equation in standard form

`(25(x-1)^(2))/(100)+(4y^(2))/(100)=(100)/(100)`

Simplify

`((x-1)^(2))/(4)+(y^(2))/(25)=1`