What is the equation of a circle centered about the origin with a radius of 6?

Select one:
A. (x)2 + (y)2 = 6
B. (x)2 − (y)2 = 6
C. (x)2 + (y)2 = 36
D. (x)2 − (y)2 = 36
E. (x)2 + (y)2 = 12

The radius of the circle is √74

Step-by-step explanation:

Radius of a circle is the distance between the centre of a circle and its circumference.

The origin of the circle (0,0) will be its centre.

The point on the edge of the circle is the point on its circumference which is (5,7).

The radius of the circle will be the distance between this two points according to definition.

R = √(x2-x1)²+(y2-y1)²

Given (x1, y1) = (0,0) and (x2, y2) = (5, 7)

x1 = 0, y1 = 0, x2 = 5, y2 = 7

Substituting into the formula we have;

R = √(5-0)²+(7-0)²

R = √5²+7²

R = √25+49

R = √74

Step-by-step explanation:

Given that a centre has an origin (0,0) and (5,7) at the edge.

What is the radius of the circle

This is a direct question, we can apply coordinate geometry by finding the distance between two point, .

From co-ordinate geometry, the distance between two points is

d =√[(x2-x1)² + (y2-y1)²]

So, applying this

Point 1 = (x1,y1) = (0,0)

Point 2 = (x2,y2) = (5,7)

The radius of the is

r = √[(x2-x1)² + (y2-y1)²]

r = √[(5-0)² + (7-0)²]

r = √[5² + 7²]

r = √(25 + 49)

r = √74

The correct answer is D

D. √74

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction