How do you convert $7 x + 10 y = 0$ $7 x+10 y = 0$ to polar form?

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Answer 1 · 2016-08-28T07:09:08

$θ + a r c tan (0.7) = 0$ $theta+arc tan(0.7)=0$ .

To convert a cartesian eqn. into a polar, we need the following

conversion formulae $: x = r cos θ, y = r sin θ$ $: x=rcos theta, y=rsin theta$ , where, $r > 0$ $r>0$ and, $θ \in (- π, π]$ $theta in (-pi,pi]$ .

Sub. ing these in the given cartesian eqn., we get,

$7 (r cos θ) + 10 (r sin θ) = 0$ $7(rcos theta)+10(rsin theta)=0$

Since $r \neq 0, we have, 10 sin θ = - 7 cos θ, or, tan θ = - \frac{7}{10}$ $r!=0, "we have," 10sin theta=-7cos theta, or, tan theta=-7/10$

$:. theta=arc tan(-7/10)=-arc tan(0.7)$ . Hence,

$theta+arc tan(0.7)=0$ is the reqd. polar eqn.

How do you convert 7 x+10 y = 07x+10y=07 x+10 y = 0 to polar form?