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

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a point of straight lines

an ellipse

a hyperbola

a rectangular hyperbola.

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Correct option is C

x52−y2=4⇒x2100−y24=1which is a hyperbola.

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Let $P (x, y)$ be a variable point such that $|\sqrt{(x - 3)^{2} + (y - 2)^{2}} - \sqrt{(x - 6)^{2} + (y + 2)^{2}}| = 3 .$

Statement-1: $P$ traces a hyperbola whose eccentricity is $\frac{5}{3}$ .

Statement-2: $P$ traces a hyperbola such that the equation of its conjugate axis is $6 x - 8 y = 27$

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The curve represented by x=5t+1t, y=t−1t,t≠0 is

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