What is the equation of the circle with center (4, 4) that passes through the point (10, 14)?

A) - 4)2 + (y + 4)2 = 32
B) (x + 4)2 + (y - 4)2 = 48
C) (x - 4)2 + (y - 4)2 = 64
D) (x – 4)2 + (y - 4)2 = 136

You use the given information in the standard form of a circle equation to solve for r. We have (h, k) which is the center and a point (x, y). The standard equation for a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Filling in:

[tex](10-4)^2+(14-4)^2=r^2[/tex] and

[tex]6^2+10^2=r^2[/tex] and

[tex]r^2=136[/tex]

Now that we used the coordinate we don't need it anymore. x and y go back into the equation as x and y, not numbers. We do, however, need the center. Writing the equation:

[tex](x-4)^2+(y-4)^2=136[/tex] which is choice D.

What is the equation of the circle with center (4, 4) that passes through the point (10, 14)? A) - 4)2 + (y + 4)2 = 32 B) (x + 4)2 + (y - 4)2 = 48 C) (x - 4)2 + (y - 4)2 = 64 D) (x – 4)2 + (y - 4)2 = 136

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What is the equation of the circle with center (4, 4) that passes through the point (10, 14)?

A) - 4)2 + (y + 4)2 = 32
B) (x + 4)2 + (y - 4)2 = 48
C) (x - 4)2 + (y - 4)2 = 64
D) (x – 4)2 + (y - 4)2 = 136