Application Of Derivatives Ques 10

10. If the line $a x+b y+c=0$ is a normal to the curve $x y=1$, then

(a) $a>0, b>0$

(b) $a>0, b<0$

(c) $a<0, b>0$

(d) $a<0, b<0$

$(1986,2 \mathrm{M})$

Show Answer

Answer:

Correct Answer: 10.(b, c)

Solution:

Formula:

Equation of tangent and normal :

  1. Given,

$\Rightarrow \quad \frac{d y}{d x}=-\frac{1}{x^{2}}$

Thus, slope of normal $=x^{2}$ (which is always positive) and it is given $a x+b y+c=0$ is normal, whose slope $=-\frac{a}{b}$.

$\Rightarrow \quad-\frac{a}{b}>0 \quad$ or $\quad \frac{a}{b}<0$

Hence, $a$ and $b$ are of opposite sign.

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