Question

If the parametric equation of a circle are $x=-4+5\cos \theta$ and $y=-3+5\sin \theta$, then which of the following is/are true

• A. centre of circle is $(4,3)$
• B. centre of circle is $(-4,-3)$
• C. area of circle is $25\pi$ sq.units
• D. perimeter of circle is $10\pi$ units

Answer 1

Answer: (B), (C), (D)

The correct options are
B centre of circle is $(-4,-3)$
C area of circle is $25\pi$ sq.units
D perimeter of circle is $10\pi$ units

Given parametric equations
$x=-4+5\cos \theta$ and $y=-3+5\sin \theta$
$\Rightarrow x+4=5\cos \theta \dots \left(1\right)$ and $y+3=5\sin \theta \dots \left(2\right)$
squaring and adding both equations, we get
$(x+4{)}^2+(y+3{)}^2=5^2$
$\Rightarrow$ centre$=(-4,-3)$ and radius$=5$
$\therefore$ Area$=\pi r^2=25\pi$
and perimeter$=2\pi r=10\pi$