Carcass wrote:

In the xy-plane, a circle is centered at the point (-4,3) and passes through the origin. What is the area of the circle?

A. 9π

B. 12π

C. 16π

D. 20π

E. 25π

kudo for the right solution and explanation

Here,

Since the co-ordinates for the centre of the circle = (-4,3)

and it passes through the orgin i.e co ordinates are =(0,0)

NOw the distance from (-4,3) to point (0,0) will give the radius of the circle

Distance between two points (x1,y1) and (x2,y2) in the xy plane = \(\sqrt{{(x2 - x1)^2 + (y2 - y1)^2}}\)

Therefore the distance between (-4,3) and (0,0) = \(\sqrt{{(0 - (-4))^2 + (0 - 3)^2}}\)

=\(\sqrt{25}\) = 5

SInce Area of the circle = \(\pi * (radius)^2\)

= \(\pi * 5^2\)

=\(25\pi\) i. e option E

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