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Secant of a Curve y =f(x)

The number of...

Question

The number of lines which are normal to the hyperbola $x y = c^{2}$ and tangent to the hyperbola $x y = - c^{2}$ , is

Z e r o

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T w o

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F o u r

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I n f i n i t e l y m a n y

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Solution

The correct option is A $Z e r o$
$\begin{matrix} x y^{1} + y = 0 y^{1} = \frac{y}{x} n o r m a l s l o p e = \frac{x}{y} x y^{1} = 0 y^{1} = - \frac{y}{x} h a v e s l o p e ∴ o n l y o n e l i n e \end{matrix}$

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