Question

The letters x and y represent rectangular coordinates. Write the following equation using polar coordinates (r, θ).

x^2 + 4y^2 = 4

Answer 1

Is my answer:

\[\cos^2\theta+4\sin^2\theta=4r\]

Answer 2

To engineer the necessary conversion:

1) replace "x" with "r cos theta."
2) replace "y" with "r sin theta."
3) Leave the constant (4) alone. Why multiply it by "r?"

Answer 3

@mathmale

Ohhhh okay.

So it should be -

\[r^2(\cos^2\theta +4\sin^2\theta) = 4\]