Parabola Part 1

The mirror image of any point (α,β) with respect to line y=x is simply (β,α).
Let (h,k) be the mirror image of a point on parabola y2=4ax Then, (k,h) will be the mirror image of (h,k) and it will lie on parabola.
SO y2=4x
h2=4k
⇒‌‌x2=4y
Hence, Locus is x2=4y....(i)
For finding equation of tangent differentiate Eq. (i) w.r.t. x
2x=4‌

dy

dx

⇒‌‌‌

y−1

x−2

=1⇒y−1=x−2
y=x−1
∴ Equation of tangent ⇒y=x−1
⇒‌‌x−y=1