r 45 3 sin theta r 82 5 cos theta Find equation in both

r = 4/5 - 3 sin theta r = 8/2 - 5 cos theta Find equation in both rectangular and parametric form

Solution

a ) Given that

r = 4 /( 5 - 3sin )

We know that

In rectangular form , r² = x² + y² , x = rcos , y = rsin

r = ( x² + y² )^1/2

r = 4 /( 5 - 3sin )

r ( 5 - 3sin ) = 4

5r - 3rsin = 4

5 ( x² + y² )^1/2 - 3y = 4

Therefore,

Rectangular form is 5 ( x² + y² )^1/2 - 3y = 4

2 ) Given that

r = 8/( 2-5cos )

r ( 2-5cos ) = 8

2r - 5rcos = 8

2( x² + y² ) ^1/2 - 5x = 8

Therefore,

Rectangular form is  2( x² + y² ) ^1/2 - 5x = 8