Question

Rewrite the equation of each circle in Standard Form. Then graph.

Answer 1

Answer:

$(x + 5) ^ 2 + (y-0) ^ 2 = 2 ^ 2$

Step-by-step explanation:

The standard form for the equation of a circumference is:

$(x-a) ^ 2 + (y-b) ^ 2 = r ^ 2$

Where:

(a, b) is the center of the circumference

r is the radius

In this problem we have the equation of the following circumference, and we want to convert it to the standard form:

$x ^ 2 + y ^ 2 + 10x +21 = 0$

The first thing we must do to transform this equation into the standard form is to use the square completion technique.

The steps are shown below:

1. Group all the same variables:

$y ^ 2 + (x ^ 2 + 10x) = -21$

2. Take the coefficient that accompanies the variable x. In this case the coefficient is 10. Then, divide by 2 and the result elevate it to the square.

We have:

$\frac{10}{2} = 5\\\\(\frac{10}{2}) ^ 2 = 25$

3. Add on both sides of the equality the term obtained in the previous step:

$y ^ 2 + (x ^ 2 + 10x +25) = -21 +25\\\\y ^ 2 + (x ^ 2 + 10x +25) = 4$

4. Factor the resulting expression, and you will get:

$(x + 5) ^ 2 + y ^ 2 = 4$

Write the equation in the standard form:

$(x + 5) ^ 2 + (y-0) ^ 2 = 2 ^ 2$

Then, the center is the point (5, 0) and the radius is r = 2.

Observe the attached image

Answer 2

Answer:

(x+5)² +  (y-0)² =2²

Step-by-step explanation:

We have given the equation:

x²+y²+10x+21=0

We have to rewrite the equation in of circle in standard form.

The standard form of circle equation is:

(x-a)² + (y-b)² =  r²

Where (a,b) is center of circle and r is the radius.

x²+y²+10 x+21=0

x²+y² +10x = -21

x² + 2(x)(5)+( 5)² + y² = -21 +(5)²  

(x+5)² + y² =  4

(x+5)² +  (y-0)² =2²

Comparing with standard equation we get,

The center is (5,0) and radius is 2.