How is the distance formula related to the equation of a circle?

is the required equation of a circle .

Step-by-step explanation:

We know that distance formula is the distance between any two points is given by:

⇒

⇒

Now, In equation of circle , Suppose we have center at  and arbitrary point in the circle is  . Distance between any point at circle to it's center is radius of circle i.e. r  , putting these values in distance formula we get:

⇒

⇒

⇒ , which the required equation of a circle .

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15