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ikadub [295]
3 years ago
7

Find a cartesian equation for the curve and identify it. r = 10 tan(θ) sec(θ)

Mathematics
1 answer:
Vilka [71]3 years ago
3 0
For a cartesian equation
x=r\cos\theta \ and \ y=r\sin\theta \\  \\ \cos\theta=\frac{x}{r} \ and \ \sin\theta=\frac{y}{r} \\  \\ \tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{y}{r}\cdot\frac{r}{x}=\frac{y}{x} \\  \\ \sec\theta=\frac{1}{\cos\theta}=\frac{r}{x}

Given r = <span>10 tan(θ) sec(θ)
r=10\tan\theta\sec\theta=10\cdot\frac{y}{x}\cdot\frac{r}{x} \\  \\ \Rightarrow10y=x^2 \\  \\ \Rightarrow y= \frac{1}{10} x^2

Therefore,</span>the curve is a parabola opening upward with vertex (0, 0).
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