Question:
If the parametric form of the circle is \( x = 3\cos\theta + 3 \) and \( y = 3\sin\theta \), then the Cartesian form of the equation of the circle is:
If the parametric form of the circle is \( x = 3\cos\theta + 3 \) and \( y = 3\sin\theta \), then the Cartesian form of the equation of the circle is:
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To convert parametric equations to Cartesian form, square both \( x \) and \( y \) and use trigonometric identities.
Updated On: Mar 7, 2025
- \( x^2 + y^2 - 6x = 0 \)
- \( x^2 + y^2 - 6x = 9 \)
- \( x^2 + y^2 + 6x = 9 \)
- \( x^2 + y^2 - 6x = 0 \)
- \( x^2 + y^2 - 2x - 2y = 9 \)
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The Correct Option is D
Solution and Explanation
From the given parametric equations:
\[
x = 3\cos\theta + 3 \quad {and} \quad y = 3\sin\theta
\]
Square both equations and combine:
\[
(x - 3)^2 + y^2 = 9
\]
Simplify to get the equation of the circle.
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