TS EAMCET · Maths · Pair of Lines

The line $\frac{x}{3} + \frac{y}{2} = 1$ and a pair of lines both passing through origin forms an isosceles triangle. If this pair of lines are perpendicular, then the equation of the pair of straight lines is

A $5 (x^{2} - y^{2}) + 24 x y = 0$
B $5 (x^{2} - y^{2}) - 24 x y = 0$
C $5 (x^{2} - y^{2}) + 12 x y = 0$
D $5 (x^{2} - y^{2}) - 12 x y = 0$

Verified Solution

Answer & Solution

Correct Answer

(B) $5 (x^{2} - y^{2}) - 24 x y = 0$

Step-by-step Solution

Detailed explanation

Pair of perpendicular lines passing through origin is ax2+2hxy-ay2=0 or x2+cxy-y2=0, where c=2ha tan45°=m--231+m-23=1 ⇒3m+2=±3-2m ⇒m=-5,15 Pair of perpendicular are, y+5xy-x5=0 ⇒x2-y2+-245xy=0, c=-245 ⇒5x2-y2-24xy=0

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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The line x3+y2=1 and a pair of lines both passing through origin forms an isosceles triangle. If this pair of lines are perpendicular, then the equation of the pair of straight lines is

Step-by-step Solution

The line $\frac{x}{3} + \frac{y}{2} = 1$ and a pair of lines both passing through origin forms an isosceles triangle. If this pair of lines are perpendicular, then the equation of the pair of straight lines is