TS EAMCET 7 May 2018 Shift 1 Solved Paper

Let (m,n) be the mid-point of the coordinate joining the focus (a,0) and a point left(xo,yo‌right) on the parabola as shown in the figure below. Coordinate of the mid-point is
(m,n)=(

xo+a

2

,

yo

2

)
xo=2m−a
yo=2n
since (xo,y0) lies on the parabola
y02=4axo
(2n)2=4a(2m−a)
n2=2a(m−

a

2

)
Therefore, the equation of the parabola is
y2=2a(x−

a

2

)
And the equation of the directrix is
x−

a

2

=−

a

2

x=0