Find the polar equation of the circle which passes through the pole and the two points whose polar coordinates are (d,0) and (2d,r/3)

Question

angela210793 · Answer

I don't remember them at all...my hs teacher never paid attention to these :( Sorry...

eyust707 · Answer

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eyust707 · Answer

not exactly sure how to come up with an equation. that satisfies that... seems odd?

eyust707 · Answer

you certinly could...

anonymous · Answer

(d,0) and (2d cosr/3, 2d sinr/3)
$$x^2 + y^2 + 2gx + 2fy = 0$$

anonymous · Answer

As the circle passes from the origin the Constant is zero.

anonymous · Answer

x-Intercept and y intercept of the circle are -2g, -2f respectively. Since -2g= d, g = -d/2.

anonymous · Answer

Now get the points in the equation and you will get the value of f.

anonymous · Answer

It would have been neater and easier if r was pi.

anonymous · Answer

I'm sure @FoolForMath has a better way to do it.

dumbcow · Answer

you could also start with a general polar equation for a circle
$$r = Acos(\theta)+Bsin(\theta)$$
plug in the 2 given points to find A and B
$$A = d$$
$$B = \frac{d(2-\cos(r/3))}{\sin(r/3)}$$
also i'm assuming r is just a constant and not the dependent variable "r" used in polar equations