Question

Find a polar equation for the curve represented by the given cartesian equation. x2 + y2 = 10cx

Answer 1

The usual rectangular to polar substitutions can be used:
  x = r·cos(θ)
  y = r·sin(θ)

These give
  r² = 10c·r·cos(θ)
or
  r = 10c·cos(θ)

Answer 2

Answer:

The polar equation for the curve represented by the given cartesian equation is $r=(10c)cos(\theta)$

Step-by-step explanation:

We were given the following equation:

$x^2+y^2=10cx$

and the relations between cartesian and polar coordinates are given by

$x=rcos(\theta)$

$y=rsin(\theta)$

where r is a radius and θ an angle. Now we replace this relations in the original cartesian equation:

$(rcos(\theta))^2+(rsin(\theta))^2=(10c)rcos(\theta)\Leftrightarrow r^2cos^2(\theta)+r^2sin^2(\theta)=(10cr)cos(\theta)\Leftrightarrow r^2(cos^2(\theta)+sin^2(\theta))=(10cr)cos(\theta)$

and we use that

$(cos^2(\theta)+sin^2(\theta))=1$

to simplify, then

$r^2=(10c)rcos(\theta)\Leftrightarrow r=(10c)cos(\theta)$

wich is the polar equation for the curve.