MereTeacher

JEE • NEET • FOUNDATION

JEE Previous Year Question

$For l \in R, the equation (2 l - 3) x^{2} + 2 l xy - y^{2} = 0 represents a pair of distinct lines$

Topic: JEE PYQ

Answer: D. Full step-by-step solution below.

A $only when l = 0$
B $for all values of l \in (- 3, 1)$
C $for all values of l \in R - (0, 1)$
D $for all values of l \in R - [- 3, 1]$

Correct answer: D

Solution

(d) a x^{2} + 2 h xy + b y^{2} = 0 represents distinct lines if h^{2} - ab > 0 ∴ l^{2} + (2 l - 3) > 0 l^{2} + 2 l - 3 > 0 (l + 3) (l - 1) > 0 ∴ l \in (- \infty, - 3) \cup (1, \infty) or l \in R - [- 3, 1]

More Straight Lines PYQs

$Suppose the hypotenuse and its opposite vertex of an isosceles right angled triangle are 3 x + 4 y - 4 = 0 and\dots$
$Let A (a, b), B (3, 4) and (- 6, - 8) respectively denote the\dots$
$The lines p (p^{2} + 1) x - y + q = 0 and (p^{2} + 1)^{2} x + (p^{2} + 1) y + 2 q = 0 are perpendicular to a line L for$
$The sum of the squares of the intercepts made the line 5 x - 2 y = 10 on the coordinate axes equals$
$Slope of a line passing through P (2, 3) and intersecting the line x + y = 7 at a distance of 4 units from P, is\dots$