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find the rectangular equation of the curve whose polar equation is r=8/(1+4cosA)

Question

Find the rectangular equation of the curve whose polar equation is r=81+4cos⁡θ r = \frac{8}{1 + 4\cos \theta}

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Solution

Sure, here are the steps to convert the polar equation r = 8/(1+4cosA) to a rectangular equation:

  1. Recall the polar to rectangular conversions: x = rcosA and y = rsinA. We will use these to substitute for r and A in the equation.

  2. First, solve the polar equation for r: r = 8/(1+4cosA).

  3. Substitute x = rcosA and y = rsinA into the equation. This gives us: x = (8cosA)/(1+4cosA) and y = (8sinA)/(1+4cosA).

  4. To eliminate A, we can use the identity sin^2A + cos^2A = 1. This gives us: (y^2)/(64) + (x^2)/(64) = 1.

  5. Simplify the equation to get the rectangular equation: x^2 + y^2 = 64.

So, the rectangular equation of the curve whose polar equation is r = 8/(1+4cosA) is x^2 + y^2 = 64.

This problem has been solved

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