Find the center-radius form for the circle having the endpoints
left parenthesis 7 comma 4 right parenthesis(7,4)
and
left parenthesis negative 9 comma 6 right parenthesis(−9,6)
of a diameter.

  (x +1)² +(y -5)² = 65

Step-by-step explanation:

The center is the midpoint of the diameter, the average of the end points:

  C = ((7, 4) +(-9, 6))/2 = ((7-9)/2, (4+6)/2) = (-1, 5)

The formula for center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

We can find r² by substituting one of the diameter end points for (x, y) and the center for (h, k).

  (7 +1)² +(4 -5)² = r² = 65

Then the circle's equation is ...

  (x +1)² +(y -5)² = 65

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

yes

step-by-step explanation: