A Circle with Center at (2,5) passes through the point (-1,4). Find the equation.?

Question

So far, its (x-2)^2+(y-5)^2=r; How do you get the radius? Show how you got it.

Answer 1

Since you have the equation the radius is found like this....

Since the radius of a circle of is distance from the center of a circle to the outside of the circle the radius can be found by finding the distance between (2,5) and (-1,4)....

There is a formula for this....
The square root of the following quantiy:
[(x1 - x2)^2 + (y1 - y2)^2]

An ordered recall is (x,y)
The subscripts on x an y tell you which ordered pair the x or y value comes from. For example:

(2,5) = (x1, y1)
This makes x1 = 2 and y1 = 5

(-1,4) = (x2, y2)
This makes x2 = -1 and y2 = 4

Returning to our equation:
The square root of the following quantiy:
[(x1 - x2)^2 + (y1 - y2)^2]

Substitute x1, x2, y1, and y2:
You get the following:

The square root of the following quantiy:
[(2 - (-1))^2 + (5 - 4)^2]

If you simplify further you get:
The square root of the following quantiy:
[(3)^2 + (1)^2]

Simplifty further by getting squaring 3 and 1
The square root of the following quantiy:
[9 + 1]

Simplifty further by adding 9 and 1
The square root of the following quantiy:
[10]

Now if you take the square root of 10 you get
3.16227766

Therefore the radius is the square root of ten or 3.16227766

By the way in the equation of a circle r needs to be sqaured Giving the the final equation of:

(x-2)^2+(y-5)^2=r^2
or....
(x-2)^2+(y-5)^2=10

Note: Since sqaure a number undoes the sqaure root this is why r^2 = 10

Answer 2

First: take (-1, 4) and place the numbers in the given formula >

(-1 - 2)^2 + (4 - 5)^2 = r
(-3)^2 + (-1)^2 = r
9 + 1 = r
10 = r
r = 10
r = V`10

(*V` represents the radical sign/square root)

Answer 3

Actually, its: (x-2)²+(y-5)²=r²;
your (x,y) is (-1,4), plugging in gives you:
(-1-2)²+(4-5)²=r²;
9+1=r²;
r=√(10)

Answer 4

So far so good, except I think it's supposed to equal r-squared. You might want to check that.

You'd need to use the distance formula with the two points you have to find the length of the radius

d = sqrt( (y2-y1)^2 + (x2-x1)^2 )

Answer 5

(-1 - 2)^2 + (4 - 5)^2 = r^2
(-3)^2 + (-1)^2 = r^2
9 + 1 = r^2
10 = r^2

(x - 2)^2 + (y - 5)^2 = 10

Radius = sqrt(10)

Answer 6

The equation is this:
(x-2)^2+(y-5)^2=r^2

Radius formula:
r=√(x2-x1)^2+(y2-y1)^2
r=√(-1-2)^2+(4-5)^2
r=√(-3)^2+(-1)^2
r=√9+1
r=√10