Question

This is so important please help

Answer 1

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

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

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

$r=\sqrt{(2-(-1))^2+(-4-0)^2}$

$r=\sqrt{(2+1)^2+(-4)^2}$

$r=\sqrt{(3)^2+(-4)^2}$

On further simplification, we get

$r=\sqrt{9+16}$

$r=\sqrt{25}$

$r=5$

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., $(x+1)^2+y^2=25$.