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This is so important please help

This is so important please help-example-1

1 Answer

5 votes

Given:

The center of the circle = (-1,0)

Point on the circle = (2,-4).

To find:

The equation of the circle.

Solution:

Distance between two points is


d=√((x_2-x_1)^2+(y_2-y_1)^2)

Distance between the center (-1,0) and the point on the circle (2,-4) is the radius of the circle.


r=√((2-(-1))^2+(-4-0)^2)


r=√((2+1)^2+(-4)^2)


r=√((3)^2+(-4)^2)

On further simplification, we get


r=√(9+16)


r=√(25)


r=5

Now, the equation of the circle is


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

Where, (h,k) is the center and r is the radius of the circle.

The radius of the circle is 5 and the center is at (-1,0), so the equation of the circle is


(x-(-1))^2+(y-0)^2=5^2


(x+1)^2+y^2=25

Therefore, the first option is correct, i.e.,
(x+1)^2+y^2=25.

User Milind Dalvi
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