normal for a parabola

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

4 Answers

q1.) is the ans
y= -x²/(y+c) +2a + a(y+c)²/x² ?

sky u r correct. please post ur approach.its enuf for me.

okie :)

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 :)

q2 ) 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...

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