Question

Convert the rectangular equation to polar form. X2 y2 = 64

Answer 1

The polar form of the equation represents all the points with a distance of 8 from the origin, which is a circumference with a radius of 8, centered on the origin.

What is the polar form of the equation?

The polar form is represented with the aid of polar coordinates of real and imaginary numbers in the coordinate system.

The horizontal and the vertical axis of the polar form denote the real axis and the imaginary axis, respectively.

The given equation to polar form is;

$\rm x^2+y^2=64$

Using the formulae that link Cartesian to Polar coordinates.

x = rcosθ and y = rsinθ

Substitute these values into the equation.

$\rm x^2+y^2=64\\\\(rcos\theta)^2+(rsin\theta)^2=64\\\\r^2cos^2\theta +r^2sin^2\theta =64\\\\r^2(cos\theta^2+sin\theta^2)=64\\\\Where ; \ sin^2\theta + cos^2\theta=1\\\\r^2(1)=64\\\\ r^2=8^2\\\\r=8$

Hence, the polar form of the equation represents all the points with a distance of 8 from the origin, which is a circumference with a radius of 8, centered on the origin.

Learn more about polar form here;

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