The curve described parametrically by y - B tan- and x - A - representsA- EllipseB- ParabolaC- HyperbolaD- Circle

The correct option is C HyperbolaEliminating the parameter θ using ^2 θ tan ^2 θ=1 (xA)^2 (yB)^2=1 ⇒x^2A^2 y^2B^2=1 Which is standard form of a hyperbola. ...

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Standard XII

Mathematics

Parametric Representation: Hyperbola

The curve des...

Question

The curve described parametrically by $y = B tan θ$ and $x = A sec θ$ represents

Ellipse

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Parabola

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Hyperbola

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Circle

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Solution

The correct option is C Hyperbola
Eliminating the parameter $θ$ using ${sec}^{2} θ - {tan}^{2} θ = 1$
${(\frac{x}{A})}^{2} - {(\frac{y}{B})}^{2} = 1 \Rightarrow \frac{x^{2}}{A^{2}} - \frac{y^{2}}{B^{2}} = 1$
Which is standard form of a hyperbola.

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The curve described parametrically by y=Btanθ and x=Asecθ represents

The correct option is C HyperbolaEliminating the parameter θ using sec2θ−tan2θ=1 (xA)2−(yB)2=1⇒x2A2−y2B2=1 Which is standard form of a hyperbola.

The curve described parametrically by $y = B tan θ$ and $x = A sec θ$ represents

The correct option is C Hyperbola
Eliminating the parameter $θ$ using ${sec}^{2} θ - {tan}^{2} θ = 1$
${(\frac{x}{A})}^{2} - {(\frac{y}{B})}^{2} = 1 \Rightarrow \frac{x^{2}}{A^{2}} - \frac{y^{2}}{B^{2}} = 1$
Which is standard form of a hyperbola.