Let in Δ PAB, A is (0, 0), B is (a, 0) and P is variable such that ∠ ∠ PBA is equal to three times …

Question

Let in Δ PAB, A is (0, 0), B is (a, 0) and P is variable such that ∠ ∠ PBA is equal to three times ∠ ∠ PAB the, find the locus of P.

CGP EDU Academic Team · Accepted Answer

The correct answer is CHECK THE SOLUTION.. 4x 3 – 4xy 2 – 3ax 2 + ay 2 = 0.
Sol. Let A ≡ ≡ (0, 0), B ≡ ≡ (a, 0)
P (h, k), ∠ ∠ PAB = θ θ
∠ ∠ PBA = 3 θ θ
Now tan θ θ =  … (1)
tan( π π – 3 θ θ ) =

From (1)
 ⇒ ⇒ 
⇒ ⇒ 3h 3 − − k 2 h − − 3ah 2 + ak 2 = – h 3 + 3k 2 h
4h 3 – 4k 2 h – 3ah 2 + ak 2 = 0
Locus of P(h, k) is 4x 3 – 4xy 2 – 3ax 2 + ay 2 = 0.
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