Two ends of latus rectum are given then the maximum number of parabolas that can be drawn equal area. 0b. 1c. 2d. infinite
It is 2.
The maximum number of parabola that we can draw at the same time from the given extremities of Latus rectum is 2.
The locus of point which moves such that the tangent from which to a parabola y2 =4ax are at right angle.
Let two tangents are drawn from point P.
Given equation of parabola is: y2=4ax.............(i)
We know that the locus of point P from which two perpendicular tangents are drawn to the parabola is the directrix of the parabola.
The standard equation of parabola (y - k)2 = 4p(x-h) has focus (x+h, k) and the directrix is (h - p).
From (i), we get,
h=0, k=0, p=1
Directrix of (i) is x= 0 - 1 = -1
Hence, the required locus is x= -1