The Cartesian equation for the curve and identify it. r² cos(2 Θ ) = 1 is
x² - y² = 1.
What is a Cartesian equation?
A Cartesian equation for a curve is one that is only expressed in terms of x and y.
To find the Cartesian equation for the curve
Since, [tex]\rm cos^2 \theta =2cos2\;\theta - 1[/tex], then
[tex]r^2cos2 \theta = 2^r2cos2 \theta\\\\ r^2=2(rcos \theta)2 -r^2 =2 \times 2 - (x^2+y^ 2) = x^2 - y^2,[/tex]
So the Cartesian curve is x² - y² = 1, which is a hyperbola having the lines y= ±x as asymptotes.
Thus, the Cartesian equation for the curve and identify it. r² cos(2 Θ ) = 1 is x² - y² = 1.
Learn more about the Cartesian equation
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