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Maths 2 - Polar Equations and Conic Sections

Quiz by DAVID BENSON QUIZZES

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7 questions
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  • Q1
    Find the area enclosed by the graph $r=2+\sin{4\theta}$ between $0\leq\theta\leq2\pi$
    $\frac{9}{2}\pi$
    $\frac{3}{2}\pi$
    $\frac{7}{2}\pi$
    $\frac{5}{2}\pi$
    300s
  • Q2
    Find the area enclosed by the graph $r=\sqrt{1+\cos^{2}(5\theta)}$ between $0\leq\theta\leq2\pi$
    $\frac{7}{2}\pi$
    $\frac{3}{2}\pi$
    $\frac{5}{2}\pi$
    $\frac{9}{2}\pi$
    300s
  • Q3
    Find the length of the polar curve: $r=2\cos{\theta}$ Between $0\leq\theta\leq2\pi$
    $4\pi$
    $2\pi$
    $5\pi$
    $3\pi$
    300s
  • Q4
    Find the length of the polar curve: $r=2(1+\cos{\theta})$ Between $0\leq\theta\leq2\pi$
    $\frac{7}{4}\pi$
    $\frac{3}{4}\pi$
    $\frac{9}{4}\pi$
    $\frac{5}{4}\pi$
    300s
  • Q5
    Give the correct description of a Hyperbola with eccentricity 1.5 and directrix at $y=2$
    $r=\frac{6}{2-3\cos{\theta}}$
    $r=\frac{6}{2+3\cos{\theta}}$
    $r=\frac{6}{2-3\sin{\theta}}$
    $r=\frac{6}{2+3\sin{\theta}}$
    300s
  • Q6
    Describe the coni section shown
    Question Image
    $r=\frac{2}{3-3\sin{\theta}}$
    $r=\frac{2}{3+3\sin{\theta}}$
    $r=\frac{2}{3-3\cos{\theta}}$
    $r=\frac{2}{3+3\cos{\theta}}$
    300s
  • Q7
    Describe the equation $y=1+3x$ as a polar equation in terms of r and $\theta$
    $r=\frac{1}{\sin{\theta}+3\cos{\theta}}$
    $r=\frac{1}{3\sin{\theta}+\cos{\theta}}$
    $r=\frac{1}{\sin{\theta}-3\cos{\theta}}$
    $r=\frac{1}{3\sin{\theta}-\cos{\theta}}$
    300s

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