Find a cartesian equation for the curve. r = 10 sin(θ) + 10 cos(θ)

Question

asked Nov 21, 2024 18.7k views

1 Answer

Spal · Answer 1 · 2024-11-26T07:45:56+0000

Explanation:

Multiply both sides by

${r}^(2) = 10r \sin( \alpha ) + 10r \cos( \alpha )$

Recall that

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

$x = r \cos( \alpha )$

$y = r \sin( \alpha )$

So we have

${x}^(2) + {y}^(2) = 10y + 10x$

${x}^(2) - 10x + {y}^(2) - 10y = 0$

Complete the square for both equations and we will get

${x}^(2) - 10x + 25 + {y}^(2) - 10y + 25 = 50$

$(x - 5) {}^(2) + (y - 5) {}^(2) = 50$

This is a circle with a center (5,5) and a radius of 5 times root 2.