TS EAMCET · Maths · Pair of Lines

Consider the lines $L_{1} \equiv 4 x + 5 y - 6 = 0, L_{2} \equiv 2 x + 3 y - 4 = 0, L_{3} \equiv 3 x - y + 2 = 0 .$ If the line $L_{1} = 0$ intersects the lines $L_{2} = 0$ and $L_{3} = 0$ at the points $A$ and $B$ respectively, then the combined equation of $O A$ and $O B$ is

A $26 x^{2} + 17 x y + 2 y^{2} = 0$
B $x^{2} - 2 x y + y^{2} = 0$
C $3 x^{2} + 17 x y + 2 y^{2} = 0$
D $26 x^{2} + 2 x y + 17 y^{2} = 0$

Verified Solution

Answer & Solution

Correct Answer

(A) $26 x^{2} + 17 x y + 2 y^{2} = 0$

Step-by-step Solution

Detailed explanation

We have straight linesL1≡4x+5y-6=0 ...1, L2≡2x+3y-4=0 ....2 L3≡3x-y+2=0 ...3 As given, the line L1=0 intersects the lines L2=0 and L3=0 at the points A and B respectively, Solving 1 and 2 we get point…

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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Consider the lines L1≡4x+5y-6=0, L2≡2x+3y-4=0, L3≡3x-y+2=0. If the line L1=0 intersects the lines L2=0 and L3=0 at the points A and B respectively, then the combined equation of OA and OB is

Step-by-step Solution

Consider the lines $L_{1} \equiv 4 x + 5 y - 6 = 0, L_{2} \equiv 2 x + 3 y - 4 = 0, L_{3} \equiv 3 x - y + 2 = 0 .$ If the line $L_{1} = 0$ intersects the lines $L_{2} = 0$ and $L_{3} = 0$ at the points $A$ and $B$ respectively, then the combined equation of $O A$ and $O B$ is