1. Tardigrade
  2. Question
  3. Mathematics
  4. If tangents drawn from each point on the line 3 x+4 y-11=0 upon a parabola are at right angle and chords joining points of contact on parabola for each point on line 3 x+4 y-11=0 pass through a fixed point (2,5) then length of latus rectum of parabola is equal to

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Q. If tangents drawn from each point on the line $3 x+4 y-11=0$ upon a parabola are at right angle and chords joining points of contact on parabola for each point on line $3 x+4 y-11=0$ pass through a fixed point $(2,5)$ then length of latus rectum of parabola is equal to

Conic Sections

Solution:

Clearly $3 x+4 y-11=0 $ must be directrix and(2,5) must be focus of P.B.
$ \therefore$ Length of $LR=2 \times $ (distance between focus of directrix)
$.=2 \times \frac{|3.2+4.5-11|}{5}=2 \cdot 3=6$