Question

If the tangent to the curve xy + ax + by = 0 at (1, 1) is inclined at an angle $ta{n}^{-1}2$ with x-axis, then

• A. a = 1, b = 2
• B. a = 1, b = –2
• C. a = – 1, b = 2
• D. a = – 1, b = – 2

Answer 1

The correct option is B a = 1, b = –2

Given, curve xy + ax + by = 0 ……….. (i)
(1, 1) lie on (i)
$\therefore$ 1 + a + b = 0 ………… (ii)
From Eq. (i),
$x\frac{dy}{dx}+y.1+a+b\frac{dy}{dx}=0\therefore \frac{dy}{dx}=-\frac{(a+y)}{(b+y)}\therefore \left(\frac{dy}{dx}\right)=-\frac{a+y}{b+x}=2(\because m=tan\theta )$
$-\frac{(-b)}{b+1}=2n$
[from Eq. (ii) ]
$\therefore b=2b+2b=–2$
From Eq. (ii), a = 1
Hence, a = 1, b = –2