AP EAMCET · Maths · Pair of Lines

If $' m_{1}'$ and $' m_{2}'$ , $(m_{1} > m_{2})$ are the slopes of the lines represented by $5 x^{2} - 8 x y + 3 y^{2} = 0$ , then $m_{1} : m_{2}$ equals

A $5 : 1$
B $2 : 1$
C $5 : 3$
D $3 : 2$

Verified Solution

Answer & Solution

Correct Answer

(C) $5 : 3$

Step-by-step Solution

Detailed explanation

Given that 'm1' and 'm1', m1>m2 are the slopes of the lines represented by 5x2-8xy+3y2=0. Given pair of lines passes through origin. Let 3y-m1x=0, 3y-m2x=0 are two lines represented by given equation. ⇒3y-m1x3y-m2x = 5x2-8xy+3y2…

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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If 'm1' and 'm2', m1>m2 are the slopes of the lines represented by 5x2-8xy+3y2=0, then m1:m2 equals

Step-by-step Solution

If $' m_{1}'$ and $' m_{2}'$ , $(m_{1} > m_{2})$ are the slopes of the lines represented by $5 x^{2} - 8 x y + 3 y^{2} = 0$ , then $m_{1} : m_{2}$ equals