Write the standard form of the Equation of the circle with the following  (-3,-1) and r= √10

Expert Answers
jgeertz eNotes educator| Certified Educator

The standard form of the equation of a circle is

`(x-h)^2 + (y-k)^2 =r^2`

 The horizontal (h) and vertical (k) translations represent the center of the circle. This formula comes from the distance formula where the distance between the center and each point on the circle is equal to the radius (r).

Fill the equation with the values of h and k which represent the center of the circle.

`(x+3)^2 +(y+1)^2 =r^2`

Fill in the value of r which is the radius of the circle.

`(x+3)^2 +(y+1)^2 = (sqrt10)^2`

`(x+3)^2 + (y+1)^2 =10`

Squaring an expression is the same as multiplying the expression by itself twice.

`(x+3)(x+3) + (y+1)^2 =10`

Use FOIL

`(x^2+6x+9) +(y+1)^2 =10`

`(x^2+6x+9) + (y+1)(y+1) =10`

Use FOIL again.

`(x^2+6x+9) + (y^2 +2y+1) =10`

Combine like terms and reorder the polynomial.

`x^2 +6x +y^2 +2y +10 =10`

The equation of the circle with center (-3, -1) and radius sqrt 10 = x^2 +6x +y^2 +2y +10 =10.