A set of parallel chords of the parabola `y^2=4a x` have their midpoint on any straight line through the vertex any straight line through the focus a straight line parallel to the axis another parabola

Options

A. any straight line through the vertex
B. any straight line through the focus
C. a straight line parallel to the axis
D. another parabola

Answer

C

Explanation

(3) Let point `P(at_(1)^(2),2at_(1))andQ(at_(2)^(2),2at_(2))` lie on the parabola `y^(2)=4ax`.
Here, point P and Q are variable. But the slope of chord PQ,
`m_(PQ)=(2)/(t_(1)+t_(2))`
Now, let the midpoint of PQ R(h,k). Then ,
`k=(2at_(1)+2at_(2))/(2)`
`or" "k=a(t_(1)+t_(2))=(2)/(m)`
`:." "y=(2)/(m)`
which is a line parallel to the axis of the parabola.