Double ordinate AB of the parabola y2 - 4ax subtends an angle -2 at the vertex of the parabola- then tangents drawn to parabola at A and B will intersect at

PQ is a double ordinate of the parabola $y^{2}$ = 4ax. If the normal at a point P intersects the line passing through Q and parallel to axis of the parabola at G. Then locus of G is a parabola with

Q. Tangents are drawn from any point on the line

x + 4 a = 0

to the parabola

y^{2} = 4 a x

. Then the angle subtended by the chord of contact at the vertex will be .

Join BYJU'S Learning Program

Double ordinate AB of the parabola y2=4ax subtends an angle π2 at the vertex of the parabola, then tangents drawn to parabola at A and B will intersect at

The correct option is C (−4a,0)Let A≡(at2,2at),B≡(at2,−2at).mOA=2t,mOB=−2tThus, (2t)(−2t)=−1⇒t2=4Equation of tangent through A is yt=x+at2Equation of tangent through B is −yt=x+at2⇒x=−at2⇒x=−4a⇒y=0Thus, tangents will intersect at (−4a,0).

Double ordinate $A B$ of the parabola $y^{2} = 4 a x$ subtends an angle $\frac{π}{2}$ at the vertex of the parabola, then tangents drawn to parabola at $A$ and $B$ will intersect at