Locus and its Equation
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Co-Ordinate system

88468 Let \(\mathbf{A}(2,3), \mathbf{B}(3,-6), \mathbf{C}(5,-7)\) be three points. If \(P\) is a point satisfying the condition \(P^{2}+P^{2}\) \(=2 P^{2}\), then a point that lies on the locus of \(\mathrm{P}\) is

1 \((2,-5)\)
2 \((-2,5)\)
3 \(13,10)\)
4 \((-13,-10)\)
AP EAMCET-2018-22.04.2018
Co-Ordinate system

88469 The equation of the locus of a point \(P(x, y, z)\) such that it's distance from the \(x\)-axis is equal to its distance from the plane \(x+z=1\) is

1 \(x^{2}-2 y^{2}-z^{2}+2 x z-2 x-2 z+1=0\)
2 \(x^{2}-2 y^{2}-z^{2}+2 x z-2 x-2 z-1=0\)
3 \(x^{2}+2 y^{2}+z^{2}+2 x z-2 x-2 z+1=0\)
4 \(x^{2}-2 y^{2}-z^{2}+2 x z-2 x+2 z+1=0\)
AP EAMCET-2020-21.09.2020
Co-Ordinate system

88470 A variable line passes through a fixed point \(\left(\mathrm{x}_{1}\right.\), \(y_{1}\) ) and meets the axes at \(A\) and \(B\). If the rectangle OAPB be completed, the locus of \(P\) is, ( \(O\) being the origin of the system of axes).

1 \(\left(y-y_{1}\right)^{2}=4\left(x-x_{1}\right)\)
2 \(\frac{x_{1}}{x}+\frac{y_{1}}{y}=1\)
3 \(x^{2}+y^{2}=x_{1}^{2}+y_{1}^{2}\)
4 \(\frac{x^{2}}{2 x_{1}^{2}}+\frac{y^{2}}{y_{1}^{2}}=1\)
WB JEE-2019
Co-Ordinate system

88472 A moving line intersects the lines \(x+y=0\) and \(\mathbf{x}-\mathbf{y}=\mathbf{0}\) at the points \(A, B\) respectively such that the area of the triangle with vertices \((0,0)\), A \& B has a constant area \(c\). The locus of the mid-point \(A B\) is given by the equation

1 \(\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right)^{2}=\mathrm{c}^{2}\)
2 \(\left(x^{2}-y^{2}\right)^{2}=c^{2}\)
3 \((\mathrm{x}+\mathrm{y})^{2}=\mathrm{c}^{2}\)
4 \((x-y)^{2}=c^{2}\)
WB JEE-2021
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Co-Ordinate system

88468 Let \(\mathbf{A}(2,3), \mathbf{B}(3,-6), \mathbf{C}(5,-7)\) be three points. If \(P\) is a point satisfying the condition \(P^{2}+P^{2}\) \(=2 P^{2}\), then a point that lies on the locus of \(\mathrm{P}\) is

1 \((2,-5)\)
2 \((-2,5)\)
3 \(13,10)\)
4 \((-13,-10)\)
AP EAMCET-2018-22.04.2018
Co-Ordinate system

88469 The equation of the locus of a point \(P(x, y, z)\) such that it's distance from the \(x\)-axis is equal to its distance from the plane \(x+z=1\) is

1 \(x^{2}-2 y^{2}-z^{2}+2 x z-2 x-2 z+1=0\)
2 \(x^{2}-2 y^{2}-z^{2}+2 x z-2 x-2 z-1=0\)
3 \(x^{2}+2 y^{2}+z^{2}+2 x z-2 x-2 z+1=0\)
4 \(x^{2}-2 y^{2}-z^{2}+2 x z-2 x+2 z+1=0\)
AP EAMCET-2020-21.09.2020
Co-Ordinate system

88470 A variable line passes through a fixed point \(\left(\mathrm{x}_{1}\right.\), \(y_{1}\) ) and meets the axes at \(A\) and \(B\). If the rectangle OAPB be completed, the locus of \(P\) is, ( \(O\) being the origin of the system of axes).

1 \(\left(y-y_{1}\right)^{2}=4\left(x-x_{1}\right)\)
2 \(\frac{x_{1}}{x}+\frac{y_{1}}{y}=1\)
3 \(x^{2}+y^{2}=x_{1}^{2}+y_{1}^{2}\)
4 \(\frac{x^{2}}{2 x_{1}^{2}}+\frac{y^{2}}{y_{1}^{2}}=1\)
WB JEE-2019
Co-Ordinate system

88472 A moving line intersects the lines \(x+y=0\) and \(\mathbf{x}-\mathbf{y}=\mathbf{0}\) at the points \(A, B\) respectively such that the area of the triangle with vertices \((0,0)\), A \& B has a constant area \(c\). The locus of the mid-point \(A B\) is given by the equation

1 \(\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right)^{2}=\mathrm{c}^{2}\)
2 \(\left(x^{2}-y^{2}\right)^{2}=c^{2}\)
3 \((\mathrm{x}+\mathrm{y})^{2}=\mathrm{c}^{2}\)
4 \((x-y)^{2}=c^{2}\)
WB JEE-2021
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Co-Ordinate system

88468 Let \(\mathbf{A}(2,3), \mathbf{B}(3,-6), \mathbf{C}(5,-7)\) be three points. If \(P\) is a point satisfying the condition \(P^{2}+P^{2}\) \(=2 P^{2}\), then a point that lies on the locus of \(\mathrm{P}\) is

1 \((2,-5)\)
2 \((-2,5)\)
3 \(13,10)\)
4 \((-13,-10)\)
AP EAMCET-2018-22.04.2018
Co-Ordinate system

88469 The equation of the locus of a point \(P(x, y, z)\) such that it's distance from the \(x\)-axis is equal to its distance from the plane \(x+z=1\) is

1 \(x^{2}-2 y^{2}-z^{2}+2 x z-2 x-2 z+1=0\)
2 \(x^{2}-2 y^{2}-z^{2}+2 x z-2 x-2 z-1=0\)
3 \(x^{2}+2 y^{2}+z^{2}+2 x z-2 x-2 z+1=0\)
4 \(x^{2}-2 y^{2}-z^{2}+2 x z-2 x+2 z+1=0\)
AP EAMCET-2020-21.09.2020
Co-Ordinate system

88470 A variable line passes through a fixed point \(\left(\mathrm{x}_{1}\right.\), \(y_{1}\) ) and meets the axes at \(A\) and \(B\). If the rectangle OAPB be completed, the locus of \(P\) is, ( \(O\) being the origin of the system of axes).

1 \(\left(y-y_{1}\right)^{2}=4\left(x-x_{1}\right)\)
2 \(\frac{x_{1}}{x}+\frac{y_{1}}{y}=1\)
3 \(x^{2}+y^{2}=x_{1}^{2}+y_{1}^{2}\)
4 \(\frac{x^{2}}{2 x_{1}^{2}}+\frac{y^{2}}{y_{1}^{2}}=1\)
WB JEE-2019
Co-Ordinate system

88472 A moving line intersects the lines \(x+y=0\) and \(\mathbf{x}-\mathbf{y}=\mathbf{0}\) at the points \(A, B\) respectively such that the area of the triangle with vertices \((0,0)\), A \& B has a constant area \(c\). The locus of the mid-point \(A B\) is given by the equation

1 \(\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right)^{2}=\mathrm{c}^{2}\)
2 \(\left(x^{2}-y^{2}\right)^{2}=c^{2}\)
3 \((\mathrm{x}+\mathrm{y})^{2}=\mathrm{c}^{2}\)
4 \((x-y)^{2}=c^{2}\)
WB JEE-2021
NEET DIGITAL LIBRARY
Co-Ordinate system

88468 Let \(\mathbf{A}(2,3), \mathbf{B}(3,-6), \mathbf{C}(5,-7)\) be three points. If \(P\) is a point satisfying the condition \(P^{2}+P^{2}\) \(=2 P^{2}\), then a point that lies on the locus of \(\mathrm{P}\) is

1 \((2,-5)\)
2 \((-2,5)\)
3 \(13,10)\)
4 \((-13,-10)\)
AP EAMCET-2018-22.04.2018
Co-Ordinate system

88469 The equation of the locus of a point \(P(x, y, z)\) such that it's distance from the \(x\)-axis is equal to its distance from the plane \(x+z=1\) is

1 \(x^{2}-2 y^{2}-z^{2}+2 x z-2 x-2 z+1=0\)
2 \(x^{2}-2 y^{2}-z^{2}+2 x z-2 x-2 z-1=0\)
3 \(x^{2}+2 y^{2}+z^{2}+2 x z-2 x-2 z+1=0\)
4 \(x^{2}-2 y^{2}-z^{2}+2 x z-2 x+2 z+1=0\)
AP EAMCET-2020-21.09.2020
Co-Ordinate system

88470 A variable line passes through a fixed point \(\left(\mathrm{x}_{1}\right.\), \(y_{1}\) ) and meets the axes at \(A\) and \(B\). If the rectangle OAPB be completed, the locus of \(P\) is, ( \(O\) being the origin of the system of axes).

1 \(\left(y-y_{1}\right)^{2}=4\left(x-x_{1}\right)\)
2 \(\frac{x_{1}}{x}+\frac{y_{1}}{y}=1\)
3 \(x^{2}+y^{2}=x_{1}^{2}+y_{1}^{2}\)
4 \(\frac{x^{2}}{2 x_{1}^{2}}+\frac{y^{2}}{y_{1}^{2}}=1\)
WB JEE-2019
Co-Ordinate system

88472 A moving line intersects the lines \(x+y=0\) and \(\mathbf{x}-\mathbf{y}=\mathbf{0}\) at the points \(A, B\) respectively such that the area of the triangle with vertices \((0,0)\), A \& B has a constant area \(c\). The locus of the mid-point \(A B\) is given by the equation

1 \(\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right)^{2}=\mathrm{c}^{2}\)
2 \(\left(x^{2}-y^{2}\right)^{2}=c^{2}\)
3 \((\mathrm{x}+\mathrm{y})^{2}=\mathrm{c}^{2}\)
4 \((x-y)^{2}=c^{2}\)
WB JEE-2021
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