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. (-3, 2).

b.  √65

c.  (x + 3)^2 + (y - 2)^2 = 65

Step-by-step explanation:

a.  The center is the midpoint  of the diameter PQ.

= (-10+4)/2, (-2+6)/2

= (-3, 2).

b. The radius is the distance from the center to a point on the circle.

Take the point (4, 6):

The radius = √((-3-4)^2 + (2-6)^2)

= √65.

c.  The equation of the circle is:

Using the standard form

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

it is (x - (-3)^2 + (y - 2) = 65

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

a. (-3,2)

b. sqrt(65)

c. (x + 3)² + (y - 2)² = 65

Step-by-step explanation:

Centre:

midpoint of the diameter

(h,k) = (-10+4)/2, (-2+6)/2

(h,k) = (-3,2)

Length of the diameter:

sqrt[(-2-6)² + (-10-4)²]

sqrt(260)

2sqrt(65)

Radius: ½ × diameter

Radius = sqrt(65)

Equation:

(x - h)² + (y - k)² = r²

(x - -3)² + (y - 2)² = (sqrt(65))²

(x + 3)² + (y - 2)² = 65

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

0.6, 3/5, and 6% are the 3 same portion.

but, when they're all changed to a decimal they would equal to 0.6.

hope this , good luck!