Question

write the standard form of the equation and the general form of the equation of the circle with radius r and center (h,k). then graph the circle. r = 5; (h,k)=(3,4)

Explanation:

Step1: Recall standard - form formula

The standard - form of the equation of a circle with center $(h,k)$ and radius $r$ is $(x - h)^2+(y - k)^2=r^2$.

Step2: Substitute values

Substitute $h = 3$, $k = 4$, and $r = 5$ into the standard - form formula:
$(x - 3)^2+(y - 4)^2=25$.

Step3: Expand to get general form

Expand $(x - 3)^2+(y - 4)^2=25$.
$(x - 3)^2=x^{2}-6x + 9$ and $(y - 4)^2=y^{2}-8y + 16$.
So $x^{2}-6x + 9+y^{2}-8y + 16=25$.
Combine like - terms: $x^{2}+y^{2}-6x-8y+9 + 16-25=0$.
The general form is $x^{2}+y^{2}-6x-8y=0$.

Answer:

Standard form: $(x - 3)^2+(y - 4)^2=25$
General form: $x^{2}+y^{2}-6x-8y=0$