TS EAMCET · Maths · Straight Lines

Let $A (5, - 3), B (3, - 2), C (- 1, 5)$ be three points. If $P$ is a point satisfying the condition $P A^{2} + 2 P B^{2} = 3 P C^{2}$ , then a point that lies on the locus of $P$ is

A $(- \frac{1}{7}, \frac{1}{2})$
B $(- \frac{5}{2}, - 2)$
C $(- \frac{2}{21}, \frac{31}{66})$
D $(2, \frac{37}{22})$

Verified Solution

Answer & Solution

Correct Answer

(D) $(2, \frac{37}{22})$

Step-by-step Solution

Detailed explanation

Given, A5,-3, B3,-2, C-1,5 be three points Now let point P be x,y, Also given P point satisfying the condition PA2+2PB2=3PC2, So, x-52+y+32+2x-32+y+22=3x+12+y-52 ⇒25-10x+9+6y+29-6x+4+4y=31+2x+25-10y ⇒28x-44y+18=0 So, from option only 2,3722 will satisfy the…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Let A5,-3, B3,-2, C-1,5 be three points. If P is a point satisfying the condition PA2+2PB2=3PC2, then a point that lies on the locus of P is

Step-by-step Solution

Let $A (5, - 3), B (3, - 2), C (- 1, 5)$ be three points. If $P$ is a point satisfying the condition $P A^{2} + 2 P B^{2} = 3 P C^{2}$ , then a point that lies on the locus of $P$ is