Question

The tangent at any point $P$ on the parabola $y^2=4ax$ intersects the $y-$axis at $Q.$ The tangent to the circum circle of triangle $PQS(S$ is the focus$)$ at $Q$ is

• A. a line parallel to $x-$axis
• B. $y-$axis
• C. a line parallel to $y-$axis
• D. None of these

Answer 1

Answer: (B)

$y-$axis

Given equation of parabola is
$y^2=4ax$

Let $P(a{t}^2,2at)$ be any point on the parabola.
Equation of tangent at $P$ is
$ty=x+a{t}^2$
Since the tangent meets $y-$axis at $Q$ i.e. $x=0$
$\Rightarrow y=at$
So, the coordinates of $Q$ is $(0,at).$
So, we draw the circumcircle of triangle $PQS.$
So, from the graph , its clear that $y-$axis is the tangent to the circumcircle of triangle $PQS$ at $Q.$