MHT CET · Maths · Circle
The parametric equations of the circle \(x^2+y^2+2 x-4 y-4=0\) are
- A \(x=-1+3 \cos \theta, y=2+3 \sin \theta\)
- B \(x=1+3 \cos \theta, y=-2+3 \sin \theta\)
- C \(x=-1+3 \sin \theta, y=-2+3 \cos \theta\)
- D \(x=1+3 \sin \theta, y=-2+3 \cos \theta\)
Answer & Solution
Correct Answer
(A) \(x=-1+3 \cos \theta, y=2+3 \sin \theta\)
Step-by-step Solution
Detailed explanation
Given equation of circle is
\(\begin{aligned}
& x^2+y^2+2 x-4 y-4=0 \\
& \Rightarrow\left(x^2+2 x+1\right)+\left(y^2-4 y+4\right)-4-5=0 \\
& \Rightarrow(x+1)^2+(y-2)^2=3^2
\end{aligned}\)
\(\therefore \quad\) Parametric equation of circle is
\(x=-1+3 \cos \theta, y=2+3 \sin \theta\)
\(\begin{aligned}
& x^2+y^2+2 x-4 y-4=0 \\
& \Rightarrow\left(x^2+2 x+1\right)+\left(y^2-4 y+4\right)-4-5=0 \\
& \Rightarrow(x+1)^2+(y-2)^2=3^2
\end{aligned}\)
\(\therefore \quad\) Parametric equation of circle is
\(x=-1+3 \cos \theta, y=2+3 \sin \theta\)
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