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  • Consider a quadratic equation in Z with parameters x and y as <img alt="\mathrm{Z}^{2}-\mathrm{xZ}+(\mathrm{x}-\mathrm{y})^{2}=0" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmath

Consider a quadratic equation in Z with parameters x and y as
\mathrm{Z}^{2}-\mathrm{xZ}+(\mathrm{x}-\mathrm{y})^{2}=0
The parameters x and y are the co-ordinates of a variable point P w.r.t. an orthonormal co-ordinate system in a plane. If the quadratic equation has equal roots then the locus of P is
 

Option: 1

a circle


Option: 2

a line pair through the origin of co-ordinates with slope 1/2 and 2/3


Option: 3

a line pair through the origin of co-ordinates with slope 3/2 and 2


Option: 4

a line pair through the origin of co-ordinates with slope 3/2 and 1/2


Answers (1)

best_answer

\mathrm{D}=0
\mathrm{x}^{2}=4(\mathrm{x}-\mathrm{y})^{2}
\mathrm{x}=2(\mathrm{x}-\mathrm{y}) \quad$ or $\quad \mathrm{x}=-2(\mathrm{x}-\mathrm{y})
\mathrm{x=2 y\: or\:3 x=2 y \Rightarrow \quad \text{ line pair with slope}\: 3 / 2\: and\: 1/2\Rightarrow \quad D}

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shivangi.shekhar

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