A circle is represented by center point [5,5] and radius 6 units. Find the parametric equation of circle and determine the various points on circle in first quadrant if increment in angle by 45o
A)9.24,9.24
B)9.42,9.42
C)9,9
D)11,5

Question

Quizplus · Accepted Answer

The parametric equations of a circle with center (h, k) and radius r are given by x = h + r*cos(θ) and y = k + r*sin(θ). For a circle centered at [5,5] with radius 6, the equations become x = 5 + 6*cos(θ) and y = 5 + 6*sin(θ). For points in the first quadrant with an angle increment of 45 degrees (π/4 radians), we calculate the coordinates using these equations. At θ = 45° (π/4 radians), cos(π/4) = sin(π/4) = √2/2. Therefore, x = 5 + 6*(√2/2) ≈ 9.24 and y = 5 + 6*(√2/2) ≈ 9.24.

A Circle Is Represented by Center Point [5,5] and Radius