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Alecsey [184]
3 years ago
12

HELP ASAP

Mathematics
1 answer:
Andrei [34K]3 years ago
7 0

Answer:

radius = \sqrt{13} or radius = 3.61

Step-by-step explanation:

Given

Points:

A(-3,2) and B(-2,3)

Required

Determine the radius of the circle

First, we have to determine the center of the circle;

Since the circle has its center on the x axis; the coordinates of the center is;

Center = (x,0)

Next is to determine the value of x through the formula of radius;

radius = \sqrt{(x_1 - x)^2 + (y_1 - y)^2} = \sqrt{(x_2 - x)^2 + (y_2 - y)^2}

Considering the given points

A(x_1,y_1) = A(-3,2)

B(x_2,y_2) = B(-2,3)

Center(x,y) =Center (x,0)

Substitute values for x,y,x_1,y_1,x_2,y_2 in the above formula

We have:

\sqrt{(-3 - x)^2 + (2 - 0)^2} = \sqrt{(-2 - x)^2 + (3 - 0)^2}

Evaluate the brackets

\sqrt{(-(3 + x))^2 + 2^2} = \sqrt{(-(2 + x))^2 + 3 ^2}

\sqrt{(-(3 + x))^2 + 4} = \sqrt{(-(2 + x))^2 + 9}

Eva;uate all squares

\sqrt{(-(3 + x))(-(3 + x)) + 4} = \sqrt{(-(2 + x))(-(2 + x)) + 9}

\sqrt{(3 + x)(3 + x) + 4} = \sqrt{(2 + x)(2 + x) + 9}

Take square of both sides

(3 + x)(3 + x) + 4 = (2 + x)(2 + x) + 9

Evaluate the brackets

3(3 + x) +x(3 + x) + 4 = 2(2 + x) +x(2 + x) + 9

9 + 3x +3x + x^2 + 4 = 4 + 2x +2x + x^2 + 9

9 + 6x + x^2 + 4 = 4 + 4x + x^2 + 9

Collect Like Terms

6x -4x + x^2 -x^2 = 4 -4 + 9 - 9

2x = 0

Divide both sides by 2

x = 0

This implies the the center of the circle is

Center = (x,0)

Substitute 0 for x

Center = (0,0)

Substitute 0 for x and y in any of the radius formula

radius = \sqrt{(x_1 - 0)^2 + (y_1 - 0)^2}

radius = \sqrt{(x_1)^2 + (y_1)^2}

Considering that we used x1 and y1;

In this case we have that; A(x_1,y_1) = A(-3,2)

Substitute -3 for x1 and 2 for y1

radius = \sqrt{(-3)^2 + (2)^2}

radius = \sqrt{13}

radius = 3.61 ---<em>Approximated</em>

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