MATH SOLVE

4 months ago

Q:
# 8x+x^2-2y-64+y^2=0 standard form with explanation

Accepted Solution

A:

x² + 8x +y² - 2y -64 =0

We see that the equation has x² and y² . Also we see that coefficients in front of x² and y² are equal. So this is an equation of the circle.

(x² + 8x) +(y² - 2y) -64 =0

(x² + 8x) +(y² - 2y) = 64

We need to complete square for x and y groups, that means it should be written in form (a+b)² or (a-b)².

Expressions in parenthesis we will write as a²+/-2ab+b², to write it after as (a+/-b)², because a²+/-2ab+b² = (a+/-b)²

(x² + 2*4x) +(y² - 2*1y) = 64

(x² + 2*4x+4²) +(y² - 2*1y+1²) = 64+4²+1²

(x+4)² + (y-1)²= 81 Sometimes this is called a standard form of the circle.

(x+4)² + (y-1)²= 9² Sometimes it is required to write like this.

And if you are studying circles,ellipses and hyperbolas, the standard form should look like

[tex] \frac{(x+4)^{2}}{9^{2}} + \frac{(y-1)^{2}}{9^{2}} =1[/tex]

We see that the equation has x² and y² . Also we see that coefficients in front of x² and y² are equal. So this is an equation of the circle.

(x² + 8x) +(y² - 2y) -64 =0

(x² + 8x) +(y² - 2y) = 64

We need to complete square for x and y groups, that means it should be written in form (a+b)² or (a-b)².

Expressions in parenthesis we will write as a²+/-2ab+b², to write it after as (a+/-b)², because a²+/-2ab+b² = (a+/-b)²

(x² + 2*4x) +(y² - 2*1y) = 64

(x² + 2*4x+4²) +(y² - 2*1y+1²) = 64+4²+1²

(x+4)² + (y-1)²= 81 Sometimes this is called a standard form of the circle.

(x+4)² + (y-1)²= 9² Sometimes it is required to write like this.

And if you are studying circles,ellipses and hyperbolas, the standard form should look like

[tex] \frac{(x+4)^{2}}{9^{2}} + \frac{(y-1)^{2}}{9^{2}} =1[/tex]