Question
What is the slope of the line tangent to the polar curve \( r=2\Theta ^{2}\) when θ = π ?
A 4π
B \(\frac{\pi }{2}\)
C \(\frac{2 }{\pi }\)
D \(-2\pi ^{2}\)
Answer/Explanation
Question
Find the polar equation of the ellipse \(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\).
(A) \(r=\frac{\cos ^{2}\Theta }{25}+\frac{\sin ^{2}\Theta }{16}\)
(B)\(r=\frac{20}{4\cos \Theta +5\sin \Theta }\)
(C) \(r=\frac{20}{\sqrt{16+9\sin ^{2}\Theta } }\)
(D)\(r=\frac{20}{4+3\sin \Theta }\)
Answer/Explanation
Ans:(C)
Question
Find the components of the vector of magnitude 6 and direction π/6 .
(A) \(\left \langle 3\sqrt{3} ,3\right \rangle\)
(B) \(\left \langle \sqrt{3} ,0\right \rangle\)
(C) \(\left \langle 2\sqrt{3} ,0\right \rangle\)
(D) \(\left \langle \pi ,\pi \right \rangle\)
Answer/Explanation
Ans:(A)
Question
Determine the symmetry of the graph of \(r=6\cos (3\Theta )\).
(A) symmetric about the x-axis, the y-axis, and the pole
(B) symmetric about the x-axis and the pole
(C) symmetric about the pole and the y-axis
(D) symmetric about the x-axis only
Answer/Explanation
Ans:(D)