write an equation for the circle that has endpoints at (1,5) and (7,11)?

Question

could you show me he equation step by step please?

Answer 1

Example - you'll need to apply it to your own endpoints.

A circle is described on the line joining (-2,5)and(3,4) as diameter, find its equation:

The equation for a circle is:
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

It is easiest to find the center first. it is the midpoint of the line and the slope is constant:
h = x1-[(x1-x2)/2] = 3 - 5/2 = 1/2
k = y1-[(y1-y2)/2] = 5 - 1/2 = 4.5

Now, find the radius using the distance formula to find the distance between the center and the endpoint or by using a right triangle where dx and dy are the lengths of the legs. I prefer the latter, but they are pretty much the same:
dx^2 + dy^2 = r^2
r^2 = (5/2)^2 + (1/2)^2= 26/4 = 13/2
By substituing back into the equation for a circle:
(x-.5)^2 + (y-4.5)^2 = (6.5)^2 = 42.25

Answer 2

A circle has no 'endpoints'.
The two points you locate in your question can have an infinite # of circles going through them.

If, on the other hand, by 'endpoints' you mean the ends of a diameter of the circle (NOT what you said at all!), then the center of the circle will be at the midpoint of the diameter and have an x and y value half way between the points given, so Xc = 4 and Yc = 8.

The radius will be 1/2 the diameter, and the diameter can be found with the pythagorean theorem, dX^2 + dY^2 = D^2. Ergo, D^2 = (7-1)^2 + (11-5)^2 = 72, so D = root 72 and R=(root 72)/2.

With the center location and the radius, the equation can now be written:

(x-4)^2 + (y-8)^2 = 18

The 18 comes from squareing (root72)/2

Answer 3

The center of the circle is the midpoint of the line segment making the diameter AB.

The midpoint formula is used to find the coordinates of the center C of the circle.

x coordinate of C = (1 + 7) /2 = 4

y coordinate of C = (5 + 11) / 2 = 8

The radius is half the distance between A and B.

r = (1/2) ([7 - 1]^2 + [11 - 1]^2 )^1/2

= (1/2)(36 + 100)^1/2

= 8

The coordinate of C and the radius are used in the standard equation of the circle to obtain the equation:

(x - 4)^2 + (y - 8)^2 = 8^2

(x - 4)^2 + (y - 8)^2 = 64

Answer 4

You mean that the diameter's endpoints are those points, right? And you want to find the equation, not he equation, right?
First, find the center of the circle by applying the midpoint formula to both of those points. The midpoint formula states that the average of the x values and the average of the y values make the x and y values for the midpoint's coordinates.
x=(1+7)/2=4
y=(5+11)/2=8
So the midpoint's coordinates are (4,8).
Next, we apply the distance formula between the midpoint and one of the endpoints to find the radius of the circle.
sqrt[(4-1)^2+(8-5)^2]=sqrt(9+9)=sqrt(18)
Now we can plug in all of the information into the formula for a circle:
(x-h)^2+(y-k)^2=r^2
where (h,k) is the center of the circle and r is the radius.
(x-4)^2+(y-8)^2=18

Answer 5

(1,5) and (7,11)
D = sqrt((7 - 1)^2 + (11 - 5)^2)
D = sqrt(6^2 + 6^2)
D = sqrt(36 + 36)
D = sqrt(72)
D = 6sqrt(2)

Radius = 3sqrt(2) or sqrt(18)

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

(x,y) = endpoint
(h,k) = center of circle

To find out where the (h,k) is, you have to find the midpoint of (1,5) and (7,11)

((1 + 7)/2),((11 + 5)/2)
(8/2),(16/2)
(4,8)

Now you have

(h,k) and (x,y), which is (4,8) and (1,5)

(x - h)^2 + (y - k)^2 = r^2
(1 - 4)^2 + (5 - 8)^2 = (sqrt(18))^2
(-3)^2 + (-3)^2 = 18
9 + 9 = 18
18 = 18

So that works out, so your equation is

(x - 4)^2 + (y - 8)^2 = 18

Answer 6

Let the center of the circle be C(a,b)

a=(1+7)/2=4
b=(5+11)/2=8
The length between C(4,8) and (1,5) will be the radius.
radius sqyare will be 18

Let any point on the circle be P(x,y)

The equation of the circle is (x-4)^2 +(y-8)^2 =18

Answer 7

Its center is the midpoint between the two points (1,5) and (7,11)
= ((x1+x2)/2 , (y1+y2)/2) = (4,8),
its radius = half the length of its diameter
= 1/2 * sqrt [(x2 - x1)^2 + ( y2 - y1)^2]
= 3 sqrt(2)
The equation is :
(x - p)^2 +(y - q)^2 = r^2
where (p,q) its center , r = rafius
(x - 4)^2 +(y - 8)^2 = 18
x^2 + y^2 - 8x - 16y + 62 = 0

Answer 8

Its center is the midpoint between the two points (1,5) and (7,11)
= ((x1+x2)/2 , (y1+y2)/2) = (4,8),
its radius = half the length of its diameter
= 1/2 * sqrt [(x2 - x1)^2 + ( y2 - y1)^2]
= 3 sqrt(2)
The equation is :
(x - p)^2 +(y - q)^2 = r^2
where (p,q) its center , r = rafius
(x - 4)^2 +(y - 8)^2 = 18
x^2 + y^2 - 8x - 16y + 62 = 0
If you need more details just ask

Answer 9

Equation is- x+y-8=4underroot2.I am unable to write underroot 2.Sorry for that.

Answer 10

lol everyone just wants other people to do their homework for them on here huh