Point P=(8,17) and Q=(-2,17) are the endpoints of the diameter of a circle a) what is the equation of the circle
b) what is the length of the arc of the circle between Point P and Point R=(0,13)
c) what is the angle formed by a sector whose area is 25/12pi

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  a) (x -3)^2 +(y -17)^2 = 25

  b) ≈ 11.07

  c) π/6 radians

Step-by-step explanation:

a) The center of the circle is the midpoint of the given segment, so is ...

  A = (P +Q)/2 = ((8, 17) +(-2, 17))/2 = (6, 34)/2 = (3, 17) . . . center

The radius is the difference between center and end coordinates: 8 -3 = 5.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)^2 +(y -k)^2 = r^2

This circle's equation is ...

  (x -3)^2 +(y -17)^2 = 25

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b) The length of the arc is given by ...

  s = rθ

where r is the circle radius and θ is the central angle in radians.

We can find the central angle using a little trigonometry. Point R differs from point A by ...

  R -A = (0, 13) -(3, 17) = (-3, -4)

so is 4 units below and 3 units left of the center of the circle. The sine of this angle QAR is 4/5, so its value is ...

  angle QAR = arcsin(4/5) ≈ 53.13°

Then angle PAR is the supplement of this, so about 126.87°, or 2.2143 radians. Then the arc length is ...

  s = (5)(2.2143 radians)

  s ≈ 11.07

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c) The area of a sector is given by ...

  A = (1/2)r^2·θ

Then the angle is ...

  θ = (2A)/r^2

For the given values and r=5, we have ...

  θ = 2(25/12π)/25

  θ = π/6

The sector with that area will have a central angle of π/6 radians, or 30°.

the equivalent expression are always the hardest ones but you look at the gcf also

step-by-step explanation: