SATHEE: Application of Derivatives 1 Question 15

Application of Derivatives 1 Question 15

15. 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) $a > 0, b < 0$

$(1986, 2 M)$

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

Fill in the Blank

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Solution:

Given,

$x y = 1 \Rightarrow y = \frac{1}{x}$

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

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

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

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

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Application of Derivatives 1 Question 15

15. If the line ax+by+c=0 is a normal to the curve xy=1, then

Fill in the Blank

Solution:

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