Let two tangents 3x-4y+20=0 and x-y-3=0 of a parabola intersect the tangent at vertex at points P(0 , 5) and Q(3 , 0) respectively, then the length of latus rectum is

Question

Let two tangents 3x-4y+20=0 and x-y-3=0 of a parabola intersect the tangent at vertex at points P(0 , 5) and Q(3 , 0) respectively, then the length of latus rectum is (A) (12/√34) (B) (18/√34) (C) (24/√34) (D) √34

Tardigrade Admin · Accepted Answer

Focus is (6 , - 3) and equation of tangent at vertex is 5x+3y-15=0 ∴ LR=4|(30 - 9 - 15/√34)|=(24/√34)

Q. Let two tangents $3 x - 4 y + 20 = 0$ and $x - y - 3 = 0$ of a parabola intersect the tangent at vertex at points $P (0, 5)$ and $Q (3, 0)$ respectively, then the length of latus rectum is

$\frac{12}{34}$

$\frac{18}{34}$

$\frac{24}{34}$

$34$

Focus is $(6, - 3)$ and equation of tangent at vertex is $5 x + 3 y - 15 = 0$
$∴ L R = 4 ∣ ∣ \frac{30 - 9 - 15}{34} ∣ ∣ = \frac{24}{34}$

Q. Let two tangents 3x−4y+20=0 and x−y−3=0 of a parabola intersect the tangent at vertex at points P(0,5) and Q(3,0) respectively, then the length of latus rectum is

34​12​

34​18​

34​24​

34​