The equation represents x2-2 x y-y2-3 x-2-0 representsA- A parabolaB- An ellipseC- A hyperbolaD- A circle

The correct option is A A parabolaΔ (1)(1)(2)+2 ( 3/2 )(0)( 1) (1)(0)^2 (1) ( 3/2 )^2 2( 1)^2 =2 9/4 2 lt;0 and h^2 ab=1 1=0 i.e., h^2=ab⇒ a parabola ...

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Standard XII

Mathematics

Standard Equation of Hyperbola

The equation ...

Question

The equation represents $x^{2} - 2 x y + y^{2} + 3 x + 2 = 0$ represents

A parabola

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An ellipse

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A hyperbola

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A circle

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Solution

The correct option is A A parabola
$Δ (1) (1) (2) + 2 (\frac{3}{2}) (0) (- 1) - (1) (0)^{2} - (1) {(\frac{3}{2})}^{2} - 2 (- 1)^{2}$
$= 2 - \frac{9}{4} - 2 < 0 a n d h^{2} - a b = 1 - 1 = 0$
i.e., $h^{2} = a b \Rightarrow a$ parabola

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The equation represents x2−2xy+y2+3x+2=0 represents

The correct option is A A parabolaΔ(1)(1)(2)+2(32)(0)(−1)−(1)(0)2−(1)(32)2−2(−1)2 =2−94−2<0 and h2−ab=1−1=0 i.e., h2=ab⇒a parabola

The equation represents $x^{2} - 2 x y + y^{2} + 3 x + 2 = 0$ represents

The correct option is A A parabola
$Δ (1) (1) (2) + 2 (\frac{3}{2}) (0) (- 1) - (1) (0)^{2} - (1) {(\frac{3}{2})}^{2} - 2 (- 1)^{2}$
$= 2 - \frac{9}{4} - 2 < 0 a n d h^{2} - a b = 1 - 1 = 0$
i.e., $h^{2} = a b \Rightarrow a$ parabola