Question

I. lf the curve $y=x^2+bx+c$ touches the straight line $y=x$ at the point $(1,1)$ then $b$ and $c$ are given by $1,1.$
II. lf the line $Px+my+n=0$ is a normal to the curve $xy=1$, then $P>0,m<0$.
Which of the above statements is correct

• A. only I
• B. only II
• C. both I and II
• D. Neither I nor II

Answer 1

Answer: (B)

only II

(I) $1+b+c=1$
$b+c=0$
$y^{\prime }=2x+b$
$y^{\prime }=1$
$2+b=1$
$(b=-1)$
$c=1$
(II) $y^{\prime }=-\frac{1}{x^2}$
$m=-\frac{1}{x^2}$
$-\frac{P}{m}=\frac{x^2}{x}$
$-P=x^{2}m$
p and m will be of opposite num.