Question

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

Answer 1

Answer:

$(x-1)^2+(y-1)^2=37.$

Step-by-step explanation:

If the center of the circle is (1,1) and the circle passes through the point (2,-5), then the radius of the circle is

$r=\sqrt{(1-2)^2+(1-(-5))^2}=\sqrt{1+36}=\sqrt{37}.$

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

$(x-1)^2+(y-1)^2=37.$

Answer 2

Answer:

(x-1)²+(y-1)² = 37 is the equation of circle.

Step-by-step explanation:

 We have given the center (1,1) and a point P (2,-5) from which the circle is passes.

So, the radius of the circle is :

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

r = $\sqrt{37}$

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-1)² = (√37)²

(x-1)²+(y-1)² = 37 is the equation of circle.