Question

write the standard form of the equation of the circle with the given center and radius.
center \\((0,0)\\), \\(r = 7\\)

the equation for the circle in standard form is
(simplify your answer.)

Explanation:

Identify the standard form equation of a circle

The standard form of the equation of a circle with center \((h, k)\) and radius \(r\) is:

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

Substitute the given values

Substitute the center \((h, k) = (0, 0)\) and radius \(r = 7\) into the standard equation:

$$(x - 0)^2 + (y - 0)^2 = 7^2$$

Simplify the equation

Simplify the terms to obtain the final standard form:

$$x^2 + y^2 = 49$$

Answer:

Write the standard form of the equation of the circle with the given center and radius.
Center \((0,0)\), \(r = 7\)

The equation for the circle in standard form is <blank>\(x^2 + y^2 = 49\)</blank>
(Simplify your answer.)