Question:
If
\[
2x^2 + 3xy - 2y^2 - 5x + 2fy - 3 = 0
\]
represents a pair of straight lines, then one of the possible values of \(f\) is?
If
\[
2x^2 + 3xy - 2y^2 - 5x + 2fy - 3 = 0
\]
represents a pair of straight lines, then one of the possible values of \(f\) is?
Show Hint
Apply the determinant condition for pair of lines in conic section to find unknown coefficients.
Updated On: Jun 6, 2025
- \(\frac{25}{2}\)
- \(25\)
- \(-5\)
- \(\frac{5}{2}\)
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The Correct Option is D
Solution and Explanation
Condition for pair of straight lines for equation
\[
Ax^2 + 2Hxy + By^2 + 2Gx + 2Fy + C = 0
\]
is
\[
\Delta = \begin{vmatrix} A & H & G \\ H & B & F \\ G & F & C \end{vmatrix} = 0.
\]
Substitute \(A=2, H=\frac{3}{2}, B=-2, G=-\frac{5}{2}, F=f, C=-3\).
Solve determinant equation for \(f\), resulting in \(f = \frac{5}{2}\).
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