Question

how would you determine a conic represented by the polar equation r=a*cos(x)+b*sin(x). then how would you convert the equation to rectangular form? please help

Answer 1

permit me to change the x in cos(x) to
theta
for a point (r,theta) on the polar graph and that same point as (x,y) on the rectangular coordinate system graph
cos(theta) =x/r and sin(theta) = y/r
and x^2 + y^2 = r^2

so r = acos(theta) + bsin(theta) gives
r = ax/r + by/r
r^2 = ax + by

Answer 2

but how would you convert that into rectangular form?

Answer 3

then r^2 = x^2 + y^2

so

x^2 + y^2 = ax + by

isn't that the form for the equation of a circle?

can you complete the square to find its radius and centre?+