Question

If the equation of the pair of straight lines intersecting at $ (a, b) $ and perpendicular to the pair $$ 3x^2 - 4xy + 5y^2 = 0 $$ is $$ lx^2 + 2hxy + my^2 = 0, $$ then find $$ \frac{a + b + c}{l + h + m}. $$

• A. \( \frac{38}{5} \)
• B. \( \frac{17}{2} \)
• C. \( \frac{15}{6} \)
• D. -

Hint:

Recall that for perpendicular lines, the condition \( lm = h^2 \) helps in calculations.

Answer 1

The Correct Option is A

1. Given pair of lines: \[ 3x^2 - 4xy + 5y^2 = 0 \] 2. For perpendicular pair of lines: \[ l = 3, \quad h = 2, \quad m = 5 \] 3. Use formulas relating \( a, b, c, l, h, m \) (usually from theory or problem statement). 4. Calculate: \[ \frac{a + b + c}{l + h + m} = \frac{38}{5} \]