First slide

Hyperbola in conic sections

Question

The curve represented by $x = 5 (t + \frac{1}{t})$ , $y = (t - \frac{1}{t}), t \neq 0$ is

Moderate

A

a point of straight lines
B

an ellipse
C

a hyperbola
D

a rectangular hyperbola.

Solution

${(\frac{x}{5})}^{2} - y^{2} = 4$ $\Rightarrow \frac{x^{2}}{100} - \frac{y^{2}}{4} = 1$
which is a hyperbola.

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