Questions
The point of intersection of the normals to the parabola at the ends of its latusrectum is
a
(0, 2)
b
(3, 0)
c
(0, 3)
d
(2, 0)
detailed solution
Correct option is B
Any point on the parabola is (at2 , 2at) where a = 1. For the latus rectum x = a ⇒ t2 = 1⇒ t = ± 1. So ends of latus rectum are (1, ± 2). Equations of the normals at these points is given by y =– tx+2at+at3⇒x+y–3=0 and x–y–3=0 which intersect at (3, 0).Talk to our academic expert!
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Locus of the point of intersection of the normals to the parabola which are at right angles is
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