Equation of normal to hyperbola x2-a2 - y2-b2 - 1 at a sec - b tan - is ax cos - - by cot - - a2 - b2-

Equation of normal to hyperbola x^2/a^2 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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Parametric Form of Normal : Hyperbola

Equation of n...

Question

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 $θ$ = $a^{2} + b^{2} .$

True

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False

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

θ

θ

θ

θ

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

If $x = a sec θ + b tan θ$ and $y = a tan θ + b sec θ$ , then $\frac{x^{2} - y^{2}}{a^{2} - b^{2}} =$ ___

The equation of normal to a hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ at a point with parameter $θ$ is

$a x c o s θ - b y c o t θ = a^{2} + b^{2}$

θ

x = a sec θ, y = b tan θ

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

a = t a n θ + c o t θ

b = t a n θ - c o t θ

a^{2} - b^{2} + (\frac{a + b}{t a n θ})

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