Question

Given center C and a point P on a circle, find its equation. C(-2, 7) and P(1, 11)
A. (x - 1)2 + (y - 11)2 = 5
B. (x + 2)2 + (y - 7)2 = 5
C. (x - 1)2 + (y - 11)2 = 25
D. (x + 2)2 + (y - 7)2 = 25

Answer 1

The answer to your question is C.


step by step:

Answer 2

The equation of a circle with center at  $C(-2, 7)$  and Point $P(1, 11)$ will be   $(x+2)^2+(y-7)^2=25$ .

What is equation of a circle ?

Equation of a circle is written in the form $(x-h)^2+(y-k)^2=r^2$ where $(h,k)$   is the center and  $r$  is the radius.

We have,

Center at  $C(-2, 7)$

i.e. $h=-2$, $k=7$,

And

Point $P(1, 11)$

i.e. $x=1$, $y=11$

Now,

To determine Radius of the circle;

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

$r^2=(1-(-2))^2+(11-7)^2$

$r=\sqrt{3^2+4^2} =\sqrt{25}$

$r=5$

So, radius of the circle is $5$ .

Now,

Equation of a circle ;

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

$(x-(-2))^2+(y-7)^2=5^2$

$(x+2)^2+(y-7)^2=25$

So, the Equation of a circle is  $(x+2)^2+(y-7)^2=25$ .

Hence, we can say that the equation of a circle with center at  $C(-2, 7)$  and Point $P(1, 11)$  is   $(x+2)^2+(y-7)^2=25$ .

To know more about Equation of a circle click here

https://brainly.com/question/23519482

#SPJ3