How do you convert $x^{2} + 5 x y + y^{2} = 7$ $x^2 + 5xy + y^2 = 7$ to polar form?

Question

How do you convert $x^{2} + 5 x y + y^{2} = 7$ $x^2 + 5xy + y^2 = 7$ to polar form?

1 Answer

Impact of this question

1948 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-01T19:25:47

$r^{2} = \frac{7}{1 + \frac{5}{2} sin 2 θ}$ $r^2=7/(1+5/2sin2theta)$

Explanation:

To convert from Cartesian to Polar coordinates use the following formulae which link them.

$∙ x = r cos θ, y = r sin θ$ $• x=rcostheta , y=rsintheta$

$\Rightarrow r^{2} {cos}^{2} θ + 5 r^{2} cos θ sin θ + r^{2} {sin}^{2} θ = 7$ $rArr r^2cos^2theta+5r^2costhetasintheta+r^2sin^2theta=7$

remove the common factor of $r^{2}$ $r^2$

$\Rightarrow r^{2} ({cos}^{2} θ + 5 cos θ sin θ + {sin}^{2} θ) = 7$ $rArrr^2(cos^2theta+5costhetasintheta+sin^2theta)=7$

Simplify using trig. identities

$∙ {sin}^{2} θ + {cos}^{2} θ = 1 and$ $• sin^2theta+cos^2theta=1" and "$

$∙ sin 2 θ = 2 sin θ cos θ$ $• sin2theta=2sinthetacostheta$

$\Rightarrow r^{2} (1 + \frac{5}{2} sin 2 θ) = 7$ $rArrr^2(1+5/2sin2theta)=7$

$\Rightarrow r^{2} = \frac{7}{1 + \frac{5}{2} sin 2 θ}$ $rArrr^2=7/(1+5/2sin2theta)$

Science

Math

Humanities

... and beyond

How do you convert $x^{2} + 5 x y + y^{2} = 7$ $x^2 + 5xy + y^2 = 7$ to polar form?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you convert x^2 + 5xy + y^2 = 7x2+5xy+y2=7x^2 + 5xy + y^2 = 7 to polar form?

1 Answer

Explanation:

Related questions

Impact of this question

How do you convert $x^{2} + 5 x y + y^{2} = 7$ $x^2 + 5xy + y^2 = 7$ to polar form?