Polar Coordinates

Polar Coordinates - Convert Functions


The line y=ax+by = ax + b in Cartesian coordinates can be written as r=13sinθ24cosθr = \frac{13}{\sin \theta - 24 \cos \theta} in polar coordinates. Assuming bb is positive, what is the value of a+ba + b?

The graph r=216sinθr= \frac{2}{1-6\sin \theta} in polar coordinates can be expressed as x2=ay2+by+cx^2 = ay^2+by+c in Cartesian coordinates, where aa, bb and cc are real numbers. What is the value of a+b+ca+b+c?

Letting θ\theta vary from 00 to 2π,2\pi, the parametric equations x=5+cosθx= 5 + \cos \theta and y=sinθy = \sin \theta represent a circle Γ1.\Gamma_1. There is a circle Γ2\Gamma_2 that is externally tangent to Γ1,\Gamma_1, tangent to the yy-axis, and centered (in Cartesian coordinates) at (10,a).(10, \sqrt{a}). What is the value of a?a?

If xx and yy satisfy x=3cosθx=3 \cos \theta and y=8+3sinθy = 8 + 3 \sin \theta, the graph of (x,y)(x, y) is a circle. If the center of this circle is (a,b)(a, b) and the radius is rr, what is the value of a+b+ra+b+r?

Which of the following Cartesian coordinate equations represents the polar equation r=14cosθ (0θ<2π)?r=14 \cos \theta\ (0 \leq \theta < 2\pi)?


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