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Convert the equation of the hyperbola from Rectangular Coordinate to Polar Coordinate for
Solution:
There are two types of coordinate system in Analytic Geometry. The first type is the Rectangular Coordinate System where the coordinates are x and y. This is a very commonly used in plotting the points and sketching the graphs. The other type is the Polar Coordinate System where the coordinates are r and θ. The radius, r is always positive in the equation unlike the angle, θ can be a positive or a negative. If θ is positive, then the angle is measured in counterclockwise direction and if θ is negative, then the angle is measured in clockwise direction.
To convert the Rectangular Coordinate System to Polar Coordinate System, let's consider a point P(x, y) in a Rectangular Coordinate System. From point P, draw a vertical line perpendicular to x-axis. The resulting figure is a right triangle with r as the hypotenuse or a distance from a point to the origin and θ is the adjacent angle of the hypotenuse from the x-axis. Use Pythagorean Theorem and trigonometric functions to convert the values of x and y into their equivalent value of r and θ as follows
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Consider the given equation above
Substitute the values of x and y as follows
