How do you convert 9r=4cos(theta)9r=4cos(θ) into cartesian form?

1 Answer
Ratnaker Mehta
Jun 15, 2016

9x^2+9y^2-4x=0.9x2+9y2−4x=0.

Explanation:

To convert from Polar form to Cartesian, we need the following formula (1) costheta=x/r, (2) sintheta=y/r,(3) r=sqrt(x^2+y^2).(1)cosθ=xr,(2)sinθ=yr,(3)r=√x2+y2.

Using (1) in the given polar eqn. we have9r=4x/r, or, 9r^2=4x,9r=4xr,or,9r2=4x, & now by (3), 9(x^2+y^2)=4x, i.e., 9x^2+9y^2-4x=0.9(x2+y2)=4x,i.e.,9x2+9y2−4x=0.

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