AB is a chord of the parabola y2=4x such that the normals at A and B intersect at the point C(9,6).
ListI(p)Length ofAB(q)Area ofΔABC(r)Distance of origin from the line throughAB(s)The area bounded by thecoordinate axes and the line through ABListII(1)20(2)134(3)13(4)4/3
A and B are two points on the parabola y2=4ax with vertex O. if OA is perpendicular to OB and they have lengths r1 and r2 respectively, then the valye of r12/3+r22/3r14/3r24/3 is
A parabola having directrix x+y+2=0 touches a line 2x+y−5=0 at (2,1). Then the semi-latus rectum of the parabola, is
The tangent to y2=ax make angles θ1andθ2 with the x-axis. If cosθ1cosθ2=λ, then the locus of their point of intersection is
If a and c are the lengths of segments of any focal chord of the parabola y2=2bx,(b>0), then the roots of the equation ax2+bx+c=0 are
Find the equation of the parabola whose focus is S(-1,1) and directrix is 4x+3y-24=0. Also its, axis , the vertex, the length, and the equation of the latus rectum.