Question

A tangent is drawn to the parabola $y^2=x$ at $(1,1)$, then the $x$ intercept of the tangent is

• A. $1$
• B. $-1$
• C. $2$
• D. $-\frac{1}{2}$

Answer 1

The correct option is B $-1$

Parabola: $y^2=x$
Slope of the tangent: $2y{y}^{\prime }=1\Rightarrow m=y^{\prime }{|}_{(1,1)}=\frac{1}{2}$
Equation of tangent: $y=\frac{1}{2}x+c$
Putting the point $(1,1)$ in the equation,
$1=\frac{1}{2}+c\Rightarrow c=\frac{1}{2}$
Tangent: $y=\frac{1}{2}x+\frac{1}{2}$
$x$ intercept of the line : $0=\frac{1}{2}x+\frac{1}{2}\Rightarrow x=-1$