Question

Which of the following represents the standard form of equation of a circle whose center is at the origin? a. 2+2= b. 2+2= 2 c. (−ℎ)2+(−)2= 2 d. (+ℎ)2+(+)2= 2

Answer 1

Answer:
`x^2+y^2=r^2`Step-by-step explanation:

The general equation of a circle with center (h, k) and radius, r, is given as:

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

If the center is at the origin:

(h, k) = (0, 0)

Substitute h = 0 and k = 0 into the general equation above

`\begin{gathered} (x-0)^2+(y-0)^2=r^2 \\ x^2+y^2=r^2 \end{gathered}`

Therefore, the standard form of the equation of a circle whose center is at the origin is:

`x^2+y^2=r^2`