Question

The center of a circle and a point on the circle are given. Write the equation of the circle in standard form.

Answer 1

Answer:

$(x-2)^2+(y+5)^2=36$

Step-by-step explanation:

The standard form of a circle is given by the equation:

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

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

We know that the center is (2, -5). So, we can substitute 2 for h and -5 for k. This yields:

$(x-(2))^2+(y-(-5))^2=r^2$

Simplify:

$(x-2)^2+(y+5)^2=r^2$

Now, we need to determine r. We know that a point on the circle is (-4, -5). Thus, we can determine r by substituting -4 for x and -5 for y. This yields:

$(-4-2)^2+(-5+5)^2=r^2$

Evaluate:

$(-6)^2+(0)^2=r^2$

Evaluate:

$36=r^2$

Hence, the radius squared is 36.

We do not actually need to solve for r, as we will square it anyways.

We will substitute 36 for r squared. Hence, our equation is:

$(x-2)^2+(y+5)^2=36$

The radius will thus be 6 units.

Answer 2

Answer:

25= (x-2)² + (y+4)²

Hope this helps!!!