Question

Write the equation of each circle given its center and a point P that it passes through

Answer 1

Answer:

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

Step-by-step explanation:

If the center of the circle is (1,-2) and the circle passes through the point (4,2), then the radius of the circle is

$r=\sqrt{(1-4)^2+(-2-2)^2}=\sqrt{9+16}=5.$

The equation of the circle with center $(x_0,y_0)$ and radius r is

$(x-x_0)^2+(y-y_0)^2=r^2.$

In your case, the equation is

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

Answer 2

Answer:

(x-1)²+ (y+2)² = 25 is the equation of circle.

Step-by-step explanation:

We have given the center (1,-2) and a point P (4,2) from which the circle is passes.

So, the radius of the circle is :

$r = \sqrt{(4-1)^{2}+(2-(-2))^{2}}=\sqrt{25}=5$

The equation of circle is :

(x - x₁)² +(y - y₁)² = r²     where (x₁,y₁) is the center of circle.

Putting the value in above equation we get,

(x-1)²+(y-(-2))² = (5)²

(x-1)²+ (y+2)² = 25 is the equation of circle.