Find the locus of the foot of the perpendicular drawn from the point (0,-c) and c>0 to the normals to the parabola x2=4ay.
Find the locus of midpoint of chord of the parabola y2=4ax such that normals at their extremities meet on the parabola
1okie :)
q1) general eqn of a normal on the given parabola:
y = mx +2a + a/m2
here slope = m
any line perpendicular to this one will have a slope : -1/m
it also passes though (0,-c)..
so write the line equation..
then, find the intersection point and eliminate m..
done :)
1q2 ) take two points : (at12, 2at1) and (at22, 2at2).
write normals at this points in terms of t.
find the intersction point (h,k) .. this satisfies k2=4ah.
u will get a relation between t1 and t2.
the midpoint is (p,q) say.. write it in terms of t1 and t2... and
eliminate t1, t2...
