Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Two pairs of straight lines have the equations y 2 + xy –12x 2
= 0 and ax 2 + 2hxy + by 2 = 0.
One line will be common among them if
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a, b)
y 2 + xy – 12x 2 = 0 ⇒ (y + 4x) (y –3x) = 0
∴ 
= 3, –4; the two pairs will have a line common if 3
of – 4 is a root of b 
+ 2h 
+ a = 0
∴ 9b + 6h + a = 0 or 16b –8h + a = 0
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
Equation of a straight line on which length of perpendicular from the origin is four units and the …
If we reduce to the form , then the value of p is
The algebraic sum of the perpendicular distances from the points (2,0), (0, 2) and (1, 1) to a vari…
The line L has intercepts a and b on the co-ordinate axes. Keeping the origin fixed, the co-ordinat…
Let 2x–3y =0 be a given line and P (sin θ θ , 0) and Q (0, cos θ θ ) be the two points. Then P and …
If the line ax + by = 1 passes through point of intersection of y = x tan α + p sec α , y sin(30 0 …