Finding equation of a circle with centre (1,7) passing through the point (-4,-5)?

Question

Finding equation of a circle with center (1,7) passing through the point (-4,-5). How do i work this out??

I know the equation of the circle but i cant figure out how to work out the radius ..

Answer 1

Note that the general equation of a circle goes as follows;

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

Where (h,k) represents the coordinates of the center of the circle, and r represents the circle's radius.

Since we're given the center to be (1,7), our equation becomes

(x - 1)^2 + (y - 7)^2 = r^2

But we still need r. That's where our given point (-4,5) comes into play. We plug in x = -4 and y = 5 into the equation to obtain r.

(-4 - 1)^2 + (-5 - 7)^2 = r^2
(-5)^2 + (-12)^2 = r^2
25 + 144 = r^2
169 = r^2
We don't need to solve for r, since we're only interested in r^2.

Therefore, the equation of our circle is

(x - 1)^2 + (y - 7)^2 = 169

Answer 2

We know that

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

where (h,k) is the center of the circle and r is the radius, in this case h=1 and k=7. In order to obtain the radius you have to find distance between two points center and the point through which circle goes.........

(-4 - 1)^2 + (-5 - 7)^2 = 169 = r^2 then r = 13

so the equation is

(x - 1)^2 + (y - 7)^2 = 13^2
On simplifying,

x^2-2x+1 + y^2-14y+49=169

=>x^2+y^2-2x-14y-119=0...........is the equation for circle

Answer 3

the eq of the circle is

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

where (h,k) is the center of the circle and r is the radius, in this case h=1 and k=7. In order to obtain the radius you just have to put the point (x,y)=(-4,-5) in the equation and it gives you radius

(-4 - 1)^2 + (-5 - 7)^2 = 169 = r^2 then r = 13

so the equation is

(x - 1)^2 + (y - 7)^2 = 13^2

Answer 4

MY DEAR FELLOW:

as you know the equation of circle that:

(x-h)^2+(y-k)^2=r^2--------------- (1)

as th center of your circle is (h,k)=(1,7)
and the circle passes through the point (-4,-5)
so u must know that any point on the circle have same distance through its center which we called as radius

now by using the distance formula between two points you can find radius:

r=sqrt {(-4-1)^2+(-5-7)^2}

solve it u will get:

r=sqrt{169}

r= 13

now put the values of r and (h,k) in equation(1)

u get:

(x-1)^2+(y-7)^2=(13)^2

x^2-2*x+1+y^2-14*y+49=169

(x)^2+(y)^2-2*(x)-14*(y)-120=0

this is your required equation of circle

Answer 5

i'm going to easily do one to instruct you the way it truly is accomplished. To calculate the radius of the circle, you are able to desire to appreciate the area from middle to an exterior element. Use pythagorean thought. substitute in x is a million, substitute in y is 9, radius is root(80 two) If this circle grow to be prevalent on the beginning place, it would by utilising x^2+y^2 = 80 two, besides the undeniable fact that it is not, it truly is prevalent at 2, -5. So the equation is (x-2)^2 + (y+5)^2 = 80 two _

Answer 6

the equation of a circle is
(x-k)^2 + (y-m)^2= (r)^2
where (k,m) are the coordinates of the circle's center

so your circles equation is (x-1)^2 + (y-7)^2 = (r)^2

there is a constraint that the cirle will path through the point
(-4,-5)

so substituting in the above circl's equation we find

(25) +(!44) = (r)^2
so r= 13

so ur final circle's equation becomes
(x-1)^2 + (y-7)^2 = (13)^2

Answer 7

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

(-4 - 1)^2 + (-5 - 7)^2 = r^2
(-5)^2 + (-12)^2 = r^2
25 + 144 = r^2
r^2 = 169
r = 13

ANS : Radius is 13, Equation is (x - 1)^2 + (y - 7)^2 = 169

Answer 8

(x- h)^2 + (y-k)^2= r^2
put h= 1, k= 7, x= -4 ,y= -5
find r