Q1. Parametric equation of circle x2 + y2 = 16 is:
(A) x = 4 cost, y = 4 sint (B) x = 2 cost, y = 2 sint
(C) x = 16 cost, y = 16 sint (D) None of these
Answers
EXPLANATION.
Equation of circle = x² + y² = 16.
As we know that,
The parametric equation of the circle x² + y² = r² are,
⇒ x = r cosθ and y = r sinθ.
⇒ Centre of circle = (0,0).
⇒ Radius of circle = 4.
⇒ Equation = x² + y² = (4)².
⇒ x = 4 cosθ and y = 4 sinθ.
Option [A] is correct answer.
MORE INFORMATION.
Equation of tangent : T = 0.
(1) = The equation of tangent to the circle x² + y² + 2gx + 2fy + c = 0 at a point (x₁ , y₁) is xx₁ + yy₁ + g(x + x₁) + f(y + y₁) + c = 0.
(2) = The equation of tangent to circle x² + y² = a² at point (x₁ , y₁) is xx₁ + yy₁ = a².
(3) = Slope form : Form condition of tangency for every value of m, the line y = mx ± a√1 + m² is a tangent of the circle x² + y² = a² and its point of contact is (-,+am/√1 + m² , ±a/√1 + m²).
Parametric equation of circle x2 + y2 = 16 is:
(A) x = 4 cost, y = 4 sin theta (B) x = 2 cos theta , y = 2 sin theta
Hence Option A is correct .
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More To Know :
The parametric equation of the circle x2 + y2 = r2 is x = rcosθ, y = rsinθ. The parametric equation of the circle x 2 + y 2 + 2gx + 2fy + c = 0 is x = -g + rcosθ, y = -f + rsinθ.