Question

a perpendicular line is drawn from focus F of the parabola x^2 =4ay to the point X on the tangent at P(2ap, ap^2). Find the locus of X

Answer 1

lets try

Answer 2

lets call the point on tangent : X (x, y)

Answer 3

x^2=4ay,

can we write the tangent equation at P(2ap, ap^2)

?

Answer 4

yes just a sec

Answer 5

okayy

Answer 6

y-ap^2 =p(x-2ap)

Answer 7

good :)

calculate the distance from Focus to the tangent

Answer 8

use the same formula we used last time :
perpendicular distance form Focus to the tangent line : (Ax1+BY1+C)/sqrt(A^2+B^2)