Question

The ends of line segment are P $(1,3)$ and Q $(1,1)$. $R$ is a point on the line segment $PQ$ such that $PR:RQ=$ $1$ :$a$ . If $R$ is an interior point of parabola $y^2=4x$, then ${}^{\prime }{a}^{\prime }$ belongs to

• A. $(0,1)$
• B. $(-\frac{3}{5},1)$
• C. $(\frac{1}{2},\frac{3}{5})$
• D. none of these

Answer 1

The correct option is A $(0,1)$

The end of line segment are $P(1,3)$ and $Q(1,1)$ $R$ is point on line segment $PQ$ such that $PR:RQ=1:a$

If $R$ is the interior point of parabola $y^2=4x$, then $a$ belongs to:

Let $R(x,y)$

$x=\frac{a+1}{a+1}=1y=\frac{3a+1}{a+1}$

If $R$ is inhibitor to parabola $y^2=4x$

$y^2-4x<0{(3a+1)}^2-4{(a+1)}^2<05a^2-2a-3<0a=1,\frac{-3}{5}a\in (\frac{-3}{5},1)Buta>0a\in (0,1)$