Question

Write the equation of the circle that passes through the given point and has a center at the origin. (Hint: You can use the distance formula to find the radius.) (0,4)

Answer 1

The equation of the circle that passes through the point (0 , 4) and has a center at the origin is x^2 + y^2 = 16.

Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (0 , 4).

radius = distance = √(x2 - x1)^2 + (y2 - y1)^2

radius = √(0 - 0)^2 + (4 - 0)^2

radius= √0 + 16

radius = 4

The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

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

where (h , k) = (0 , 0)

r = 4

(x - 0)^2 + (y - 0)^2 = 4^2

x^2 + y^2 = 16

Learn more about equation of a circle here: brainly.com/question/14150470

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