The parametric coordinates of hyperbola x-h2a2-y-k2b2-1 are h - a - k - b tan-

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The parametri...

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The parametric coordinates of hyperbola $\frac{(x - h)^{2}}{a^{2}} - \frac{(y - k)^{2}}{b^{2}} = 1$ are $(h + a sec θ, k + b tan θ) .$

True

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False

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Solution

The correct option is A True

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Similar questions

Q. Prove the following trigonometric identities.

If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x² − y² = a² − b²

A hyperbola of the form $\frac{(x - h)^{2}}{a^{2}} - \frac{(y - k)^{2}}{b^{2}} = 1$ can be parametrically represented as $(a s e c θ + h, b t a n θ + k)$

Q. Parametric coordinates of any point lying on hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

are

P (a sec θ, b tan θ) .

Q. If

(a sec θ, b tan θ)

and

(a sec ϕ, b tan ϕ)

be the coordinates of the ends of a focal chord of the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

, then

tan \frac{θ}{2} tan \frac{ϕ}{2} =

Q. Equation of normal to hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

at (a sec

θ

, b tan

θ

) is ax cos

θ

- by cot

θ

a^{2} + b^{2} .

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The parametric coordinates of hyperbola (x−h)2a2−(y−k)2b2=1 are (h+asecθ,k+btanθ).

The correct option is A True

The parametric coordinates of hyperbola $\frac{(x - h)^{2}}{a^{2}} - \frac{(y - k)^{2}}{b^{2}} = 1$ are $(h + a sec θ, k + b tan θ) .$