Point (1,8) is on a circle with central (-2,4). What is the radius of the circle.

Answer 1

Another method to consider is to use the generic equation for a circle which is:

where the center of the circle is (h, k). You can plug in h = -2 and k = 4 to get:

(x - -2)² + (y - 4)² = r² or

(x + 2)² + (y - 4)² = r²

Then you can plug in the point (1, 8) where x = 1 and y = 8:

(1 + 2)² + (8 - 4)² = r²

then solve for "r"

(3)² + (4)² = r²

9 + 16 = r²

25 = r²

r = 5

Answer 2

What is the radius of the circle.

The radius of a circle is the disance between the center and any point on the circle.

Point (1,8) is on a circle with center (-2,4).

Solving for: The radius of a circle center point.

1. Point on th circle (1,8)
2. Center of the circle (-2,4)

Using the following Formula:

The distance formula between two points (X1,Y1) and (X2,Y2)

(x2 - x1)^2 + (y2 - y1)^2

How to solve:

Use the distance formula to find he disance between the center and he given point.

Step 1 Calculate the difference in x coordinates:

The distance formula between two points (X1,Y1) and (X2,Y2)

Subtract the x coordinate of the center from the x coordinate of the point.

(x2 - x1)

x2 =-2 and x1 =1

1 - (-2) = 1 + 2 = 3 x = 3

Step 2: Calculate the difference in x coordinates:

Subtract the y coordinate of the center of the center from the y coordinate of the point.

(y2 - y1)

y2 = 4

y1 = 8

(8-4) = 4

Step 3:

Apply the distance formula:

Use the distance formula with the differences calculated in the previous steps.

r^2= (3)^2 + (4)^2

r^2 = (9) + (16)

r^2 = (25) take the square root of both sides

square root of (r^2) = square root of (25)



radius of the circle = 5

Solution:

The radius of the circle is (5)

I hope the mathematical calculations (step by step approach) was helpful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an amazing day. Doris H.

Answer 3

One way to solve this is by using Pythagorean theorem.

r² = x² + y²

x is the distance on the x axis (horizontal) and y is the distance on the y axis (vertical) and r is the radius of the circle.

Point1 is (x₁, y₁) and Point2 is (x₂, y₂) [it doesn't matter if you use Point1 or Point2 as the central point coordinates because the distance of x and y will always be positive after you square them]

where x = x₁ - x₂ and y = y₁ - y₂ and r is the radius

I will show you in both examples that it will not matter.

Example 1) Point1 is the end point and Point2 is the central point

x = (1 - -2) => 3 and y = (8 - 4) => 4

so x² = 3² => 9 and y² = 4² => 16

Now lets assign the Point1 as the central point and Point2 as the end point

x = (-2 - 1) => -3 and y = (4 - 8) => -4

so x² = (-3)² => 9 and y² = (-4)² => 16

See, they are same values

Next, add the x and y together x + y = 9 + 16 => 25

Now we have r² = 25 and finally solve for r by taking the square root of both sides.

r = 5, the radius of the circle

Answer 4

It is helpful to draw a picture. The radius will have an endpoint at the center and on the circle. To find the length use the distance formula.

d= sq root of ( x-x)^2 + (y-y)^2

sq root of (1- -2)^2 + (8-4)^2

sq root of (1+2)^2 + (8-4)^2

sq root of 3^2 + 4^2

sq root of 9+16. sq root of 25 = 5