MHT CET · Maths · Circle
The cartesian equation of the curve given by \(x=6 \cos \theta, \quad y=6 \sin \theta\) is
- A \(x^{2}+y^{2}=36\)
- B \(x^{2}+y^{2}=5\)
- C \(x^{2}+y^{2}=25\)
- D \(x^{2}+y^{2}=6\)
Answer & Solution
Correct Answer
(A) \(x^{2}+y^{2}=36\)
Step-by-step Solution
Detailed explanation
On squaring and adding both given equations, we get
\(\begin{aligned}
x^{2}+y^{2} &=36 \cos ^{2} \theta+36 \sin ^{2} \theta \\
&=36\left(\cos ^{2} \theta+\sin ^{2} \theta\right) \\
x^{2}+y^{2} &=36
\end{aligned}\)
\(\begin{aligned}
x^{2}+y^{2} &=36 \cos ^{2} \theta+36 \sin ^{2} \theta \\
&=36\left(\cos ^{2} \theta+\sin ^{2} \theta\right) \\
x^{2}+y^{2} &=36
\end{aligned}\)
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