Question

The length of the chord of the parabola x2 = 4ay passing through the vertex and having slope
Tan a is
(A) 4a Cosec a cota (B) 4a tan a sec a
(C) 4a cosa cota
(D) 4a sin a tana​

Answer 1

Equation of parabola x2=4ay

Vertex of parabola (0)=(0,0)

Equation of chord passing through vertex y−y1=m(x−x1)

Here, x1=0 and y1=0

y−0=m(x−0)

∴y=mx

Now, slope=m=tanα

Let the chord intersect the parabola at P(h,k)

Since, point P lies on chord

k=(tanα)h ………..(1)

Point P lies on parabola

h2=4ak ………(2)

Substituting equation (1) in (2)

∴h2=4a(tanα×h)

∴h2(h−4atanα)=0

∴h=0

h=4atanα

Substituting h=4atanα in equation (2), we get

∴(4a)2tan2α=4ak

∴k=4atan2α

∴p=(h,k)=(4atanα,4atan2α)