Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If x = X cos θ – Ysin θ , y = Xsin θ + Ycos θ & x 2 + 4xy + y 2 = AX 2 + BY 2 , 0 ≤ θ ≤ 
then
Text Solution
Verified by ExpertsThe correct answer is:
C
Putting values of x & y in given relation we get
(1 + 2sin2 θ )X 2 + 4cos2 θ XY + (1 – 2sin2 θ )Y 2
= AX 2 + BY 2 Comparing
cos2 θ = 0
⇒ 2 θ = 
⇒ θ = 
1 + 2sin2 θ = A
⇒ A = 3
& B = – 1
∴ | B | < | A |
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
The coordinates of a point are (0, 1) and the ordinate of another point is –3. If the distance betw…
The points (1, 3) and (5, 1) are the opposite vertices of a rectangle. The other two vertices lie o…
If the orthocenter and centroid of a triangle are (–3, 5) and (3, 3) respectively then the circumce…
If O be the origin and if the coordinates of any two points Q 1 and Q 2 be (x 1 , y 1 ) and (x 2 , …
Let 0 < α < be fixed angle. If P = (cos θ , sin θ ) & Q = {cos ( α – θ ), sin ( α – θ )}, then Q i…
(5, 3) and (cos θ , sin θ ) lie on the same side of the line 2x + y = 8 then θ lies between-