Question bank/JEE Main/Mathematics

JEE MainMathematicsModerateConic Sections

If tangents drawn from each point on the line 3x + 4y - 11 = 0
upon a parabola are at right angle and chords joining points of contact
on parabola for each point on line 3x + 4y - 11 = 0 pass through a
fixed point (2, 5) then length of latus rectum of parabola is equal to:
izR;sd fcUnq ij,d fLFkj fcUnq (2, 5) ls xqtjrh

Show answer and solution
Clearly 3x + 4y - 11 = 0 must be directrix and (2, 5) must be
focus of P.B.
∴\therefore Length of LR
= 2 × (distance betwen focus of directrix)
=2×=2.3=6= 2 \times = 2.3 = 6
gksxh rFkk (2, 5) ukfHk gksxh
∴\therefore ukfHk dh yEckbZ =
= 2× (ukfHk nwjh)
=2×∣3.2+4.5−11∣5=2.3=6= 2 \times \frac{|3.2 + 4.5 - 11|}{5} = 2.3 = 6

Source: Grass-G / M-27 Mathematics Paper 2 15 Jan.docx

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