Question

What is the area of a circle centered at (6,9) that passes through the origin?

Answer 1

★᭄ꦿ᭄Answer★᭄ꦿ᭄

The equation of a circle with center (h,k) and radius r is given by (x−h)2+(y−k)2=r2 . For a circle centered at the origin, this becomes the more familiar equation x2+y2=r2

Answer 2

Answer:

The equation of a circle with center (h,k) and radius r is given by (x−h)2+(y−k)2=r2. For a circle centered at the origin, this becomes the more familiar equation x2+y2=r2.

Because we know the circle is centered at the origin, i.e. (0,0), we can use this fact along with the point which the circle passes through (−6,−2) to find the radius. This is done using the distance formula.

r=√(x2−x1)2+(y2−y1)2

Given the points (0,0) and (−6,−2):

r=√(−6−0)2+(−2−0)2

=√36+4

√40=2√10

⇒r=2√10.

Therefore, the equation of the circle is given by:

x2+y2=(2√10)2

⇒x2