AP EAMCET · Maths · Straight Lines

Two points $A$ and $B$ with co-ordinates $(1, 1)$ and $(- 2, 3)$ are given respectively. Then, the locus of a point $P$ so that the area of $Δ P A B$ is 9 sq.units is given by _____

A $2 x + 3 y + 13 = 0 & 2 x + 3 y - 23 = 0$
B $2 x + 3 y + 23 = 0 & 2 x + 3 y - 13 = 0$
C $2 x + 3 y - 13 = 0 & 2 x - 3 y + 23 = 0$
D $2 x - 3 y + 23 = 0 & 2 x + 3 y + 13 = 0$

Verified Solution

Answer & Solution

Correct Answer

(A) $2 x + 3 y + 13 = 0 & 2 x + 3 y - 23 = 0$

Step-by-step Solution

Detailed explanation

Given, A(1,1) and B(-2,3) Let P(x,y) be the point as per given condition A(△PAB)=9 We know that, if 3 points are given then the area of triangle is given by - 12xy1111-231=9 ⇒x(1-3)-y(1+2)+1(3+2)=9×2 ⇒x(-2)-3y+5=18 ⇒-2x-3y+5=±18…

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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Two points A and B with co-ordinates (1,1) and (-2,3) are given respectively. Then, the locus of a point P so that the area of ΔPAB is 9 sq.units is given by _____

Step-by-step Solution

Two points $A$ and $B$ with co-ordinates $(1, 1)$ and $(- 2, 3)$ are given respectively. Then, the locus of a point $P$ so that the area of $Δ P A B$ is 9 sq.units is given by _____