How do you convert $9 = {(x + 5)}^{2} + {(y + 4)}^{2}$ $9=(x+5)^2+(y+4)^2$ into polar form?

Question

1559 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-02T23:11:54

$r = -(10cos(theta) + 8sin(theta))/2 + sqrt((10cos(theta) + 8sin(theta))² - 128)/2$

Expand the squares using the pattern $(a + b)² = a² + 2ab + b²$

$9 = x² + 10x + 25 + y² + 8y + 16$

Substitute the 3 following equations into the above where appropriate:

$x² + y² = r²$
$x = rcos(theta)$
$y = rsin(theta)$

$9 = r² + 10rcos(theta) + 8rsin(theta) + 41$

Write as a quadratic equation in r:

$0 = r² + (10cos(theta) + 8sin(theta))r + 32$

Use the positive root of the quadratic formula to solve for r:

$r = -b/(2a) + sqrt(b² - 4(a)(c))/(2a)$

$r = -(10cos(theta) + 8sin(theta))/2 + sqrt((10cos(theta) + 8sin(theta))² - 128)/2$

How do you convert 9=(x+5)^2+(y+4)^29=(x+5)2+(y+4)29=(x+5)^2+(y+4)^2 into polar form?