A diameter of a circle has endpoints p(-10, -2) and q(4, 6)
a. Find the center of the circle
b. Find the radius. If your answer is not an integer, express it in radical form
c. Write an equation for the circle

a) The centre of the circle is the point (-3, 2)

b) the radius of the circle is sqrt(65)

c) the equation of the circle is 65=(x+3)+(y-2)

Step-by-step explanation:

a)

To find the middle point of a segment given its coordinates we apply the following formula:

(x,y)=[(x1-x2)/2; (y1-y2)/2]

Given the coordinates (-10, -2) and (4, 6), let:

x1=-10

x2= 4

y1=-2

y2=6

Applying the formula:

(x,y)=(-10+4)/2; (-2+6)/2

(x,y)=(-6/2); (4/2)

(x,y)=(-3; 2)

b)

To find the radius we can use the distance formula:

where x1 and y1 are the coordinates of point p (one could also use point q) and x2 and y2 are the coordinates of the centre of the circle.

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

d=sqrt[(-10+3)^2+(-2-2)^2]

d=sqrt[(-7^2+-4^2]=sqrt[49+16]=sqrt[65]

c)

The equation of a circle is given by the following formula:

(x-x0)+(y-y0)=r^2

where x0 and y0 are the coordinates of the centre of the circle.

In this case:

x0=-3

y0= 2

r^2=65

Therefore, the equation for the circle is:

65=(x+3)+(y-2)

answer: 12

step-by-step explanation:

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