Maharashtra BoardEnglish MediumSTD 12 ScienceMathsPair of Straight Lines2 Marks
MCQ
Equation $3 x^2+7 x y+2 y^2+5 x+5 y+2=0$ represents
✓
Pair of straight line
B
Ellipse
C
Hyperbola
D
Circle
✓
Answer
Correct option: A.
Pair of straight line
(A) Given equation of pair of lines is $3 x^2+7 x y+2 y^2+5 x+5 y+2=0$ $a =3, b=2, c =2, f =\frac{5}{2}, g=\frac{5}{2}, h=\frac{7}{2}$ Consider $abc +2 fgh - af ^2- bg ^2- ch ^2$ $=(3)(2)(2)+2\left(\frac{5}{2}\right)\left(\frac{5}{2}\right)\left(\frac{7}{2}\right)$$-3\left(\frac{5}{2}\right)^2-2\left(\frac{5}{2}\right)^2-2\left(\frac{7}{2}\right)^2=0$ ∴ The given equation represents a pair of straight lines.
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