Magnawolf said:Homework Statement
Find a polar equation with the graph as xy=16
The Attempt at a Solution
I also tried using x = rcos[itex]\theta[/itex] and y = r sin[itex]\theta[/itex] but I can't get anything. I know it's a hyperbola.
Magnawolf said:Inversely? I'm not sure!
A polar equation for a hyperbola is an equation that describes the shape of a hyperbola in polar coordinate system. It is typically in the form of r = k/(1±ecosθ) or r = k/(1±esinθ), where k is a constant, e is the eccentricity, and θ is the angle.
To graph a hyperbola in polar coordinates, you can plot points by plugging in different values for θ in the polar equation. Then, connect the points to form a curve. You can also use a graphing calculator or online graphing tool to plot the hyperbola.
The xy=16 equation in a hyperbola represents the rectangular form of the polar equation r = k/(1±ecosθ). It is used to find the value of k in the polar equation by substituting x and y values from a point on the hyperbola.
The eccentricity of a hyperbola can be found using the xy=16 equation by rearranging it to the form e = √(1-k²/a²), where a is the distance from the center of the hyperbola to a vertex.
Yes, you can convert a polar equation for a hyperbola to rectangular form by using the trigonometric identities x = rcosθ and y = rsinθ. This will give you the rectangular form of the polar equation, which can be useful for graphing and solving equations.