An equilateral triangle PQR is formed where P (1, 3) is fixed point and Q is moving point on line x = 3. Find the locus of R.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(x – 2) = ± ± 
(y – 3 ± ± 
)
Sol. Slope of PR is ( θ θ ± ± 60 0 ).
Let coordinates of be (h, k).
= 2 sec θ θ
h = 1 + 2cos ( θ θ ± ± 60 0 ) sec θ θ
⇒ ⇒ h = 1 + 2 
…(1)
⇒ ⇒ k = 3 + 2 sin ( θ θ ± ± 60 0 ) sec θ θ
⇒ ⇒ k = 3 + 2 
…(2)
Eliminating θ θ from (1) and (2),
= ± ± tan θ θ
k – 3 ± ± 
= tan θ θ
⇒ ⇒ 
= ± ± (k – 3 ± ± 
)
Locus is (x – 2) = ± ± 
(y – 3 ± ± 
)
──────────────────────────────────────────────────────────────────────────────────────────
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