The solutions to the blanks are Circle, y-axis and 5 units, respectively.
What is the equation of the circle?
The equation of the circle whose center is coordination at (h,k) and radius is r will be
(x -h)² +(y -k)² = r²
where (h,k) is the coordination of its center and r is the radius.
We have,
r = 5 sinΘ
So,
When the center of the circle is at origin (0,0);
Then x² + y² = r²
So,
We have, r = 5 sinΘ
So,
For 0 ≤ θ ≤ π,
The circle is developed above the x-axis and symmetrical about the y-axis (θ=π/2)
The circle has a radius of 5/2, centered at (0, 5/2), so the diameter is 5 units.
And hence the greatest distance between any two points on a graph is 5 units.
Therefore, the solutions to the blanks are Circle, y-axis, and 5 units, respectively.
Learn more about the circle here:
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