How do you convert $x^{2} + y^{2} = 5$ $x^2 + y^2 = 5$ to polar form?

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Answer 1 · 2018-08-04T03:03:59

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The given equation in

Cartesian Form or Rectangular Form $x^{2} + y^{2} = 5$ $color(red)(x^2+y^2=5$

can be converted to Polar Form as:

$r = \pm \sqrt{5}$ $color(blue)(r=+- sqrt(5$

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The given equation is in

Cartesian Form or Rectangular Form $x^{2} + y^{2} = 5$ $color(red)(x^2+y^2=5$

We need the following formula to convert to Polar Form:

$r^{2} = x^{2} + y^{2}$ $color(blue)(r^2=x^2+y^2$

$\Rightarrow r = \sqrt{x^{2} + y^{2}}$ $rArr r=sqrt(x^2+y^2$

$x = r cos θ$ $color(blue)(x=r cos theta$

$y = r sin θ$ $color(blue)(y=r sin theta$

$tan θ = (\frac{y}{x})$ $color(blue)(tan theta = (y/x)$

$\Rightarrow θ = {tan}^{- 1} (\frac{y}{x})$ $rArr theta = tan^(-1)(y/x)$

We have the Cartesian form:

$x^{2} + y^{2} = 5$ $x^2+y^2=5$

Since, $r^{2} = x^{2} + y^{2}$ $color(blue)(r^2=x^2+y^2$ we can write

$r^{2} = 5$ $r^2=5$

$r = \pm \sqrt{5}$ $r = +- sqrt(5)$

This the equation in Polar Form.

Hope it helps.

How do you convert x^2 + y^2 = 5x2+y2=5 x^2 + y^2 = 5 to polar form?