Equation of Line in Different Forms
Straight Line

88672 A square is formed by the lines \(x=0, y=0, x=1\), \(y=1\). Then, the equation of its diagonals will be

1 \(y=x, x+y=2\)
2 \(2 \mathrm{y}=x, x+y=\frac{1}{2}\)
3 \(\mathrm{y}=x, x+y=1\)
4 \(y=2 x, z+y=\frac{1}{4}\)
Straight Line

88673 Find the value of ' \(k\) ' if the angle between the straight lines represented by
\(2 x^{2}+5 x y+3 y^{2}+6 x+7 y+4=0 \text { is } \tan ^{-1}(k) .\)

1 \(\left(\frac{1}{5}\right)\) only
2 \(\left(\frac{-1}{5}\right)\) only
3 \(\pm \frac{1}{5}\)
4 0
Straight Line

88689 A variable line passes through the fixed point \((\alpha, \beta)\) The locus of the foot of the perpendicular from the origin on the line is

1 \(x^{2}+y^{2}-\alpha x-\beta y=0\)
2 \(x^{2}+y^{2}+2 \alpha x+2 \beta y=0\)
3 \(\alpha x+\beta y \pm \sqrt{\left(\alpha^{2}+\beta^{2}\right)}=0\)
4 \(\frac{x^{2}}{\alpha^{2}}+\frac{y^{2}}{\beta^{2}}=1\)
Straight Line

88647 If the midpoint of the section of the straight line intercepted between the axes is \((1,1)\) then the equation of the line is

1 \(2 x+y=3\)
2 \(2 x-y=1\)
3 \(x-y=0\)
4 \(x+y=2\)
Straight Line

88648 The perpendicular distance of a line from the origin is \(7 \mathrm{~cm}\) and its slope is -1 . The equation of line is

1 \(x+y+7 \sqrt{2}=0\)
2 \(x-y+7 \sqrt{2}=0\)
3 \(x+y-7 \sqrt{2}=0\)
4 \(x-y-7 \sqrt{2}=0\)
Straight Line

88672 A square is formed by the lines \(x=0, y=0, x=1\), \(y=1\). Then, the equation of its diagonals will be

1 \(y=x, x+y=2\)
2 \(2 \mathrm{y}=x, x+y=\frac{1}{2}\)
3 \(\mathrm{y}=x, x+y=1\)
4 \(y=2 x, z+y=\frac{1}{4}\)
Straight Line

88673 Find the value of ' \(k\) ' if the angle between the straight lines represented by
\(2 x^{2}+5 x y+3 y^{2}+6 x+7 y+4=0 \text { is } \tan ^{-1}(k) .\)

1 \(\left(\frac{1}{5}\right)\) only
2 \(\left(\frac{-1}{5}\right)\) only
3 \(\pm \frac{1}{5}\)
4 0
Straight Line

88689 A variable line passes through the fixed point \((\alpha, \beta)\) The locus of the foot of the perpendicular from the origin on the line is

1 \(x^{2}+y^{2}-\alpha x-\beta y=0\)
2 \(x^{2}+y^{2}+2 \alpha x+2 \beta y=0\)
3 \(\alpha x+\beta y \pm \sqrt{\left(\alpha^{2}+\beta^{2}\right)}=0\)
4 \(\frac{x^{2}}{\alpha^{2}}+\frac{y^{2}}{\beta^{2}}=1\)
Straight Line

88647 If the midpoint of the section of the straight line intercepted between the axes is \((1,1)\) then the equation of the line is

1 \(2 x+y=3\)
2 \(2 x-y=1\)
3 \(x-y=0\)
4 \(x+y=2\)
Straight Line

88648 The perpendicular distance of a line from the origin is \(7 \mathrm{~cm}\) and its slope is -1 . The equation of line is

1 \(x+y+7 \sqrt{2}=0\)
2 \(x-y+7 \sqrt{2}=0\)
3 \(x+y-7 \sqrt{2}=0\)
4 \(x-y-7 \sqrt{2}=0\)
Straight Line

88672 A square is formed by the lines \(x=0, y=0, x=1\), \(y=1\). Then, the equation of its diagonals will be

1 \(y=x, x+y=2\)
2 \(2 \mathrm{y}=x, x+y=\frac{1}{2}\)
3 \(\mathrm{y}=x, x+y=1\)
4 \(y=2 x, z+y=\frac{1}{4}\)
Straight Line

88673 Find the value of ' \(k\) ' if the angle between the straight lines represented by
\(2 x^{2}+5 x y+3 y^{2}+6 x+7 y+4=0 \text { is } \tan ^{-1}(k) .\)

1 \(\left(\frac{1}{5}\right)\) only
2 \(\left(\frac{-1}{5}\right)\) only
3 \(\pm \frac{1}{5}\)
4 0
Straight Line

88689 A variable line passes through the fixed point \((\alpha, \beta)\) The locus of the foot of the perpendicular from the origin on the line is

1 \(x^{2}+y^{2}-\alpha x-\beta y=0\)
2 \(x^{2}+y^{2}+2 \alpha x+2 \beta y=0\)
3 \(\alpha x+\beta y \pm \sqrt{\left(\alpha^{2}+\beta^{2}\right)}=0\)
4 \(\frac{x^{2}}{\alpha^{2}}+\frac{y^{2}}{\beta^{2}}=1\)
Straight Line

88647 If the midpoint of the section of the straight line intercepted between the axes is \((1,1)\) then the equation of the line is

1 \(2 x+y=3\)
2 \(2 x-y=1\)
3 \(x-y=0\)
4 \(x+y=2\)
Straight Line

88648 The perpendicular distance of a line from the origin is \(7 \mathrm{~cm}\) and its slope is -1 . The equation of line is

1 \(x+y+7 \sqrt{2}=0\)
2 \(x-y+7 \sqrt{2}=0\)
3 \(x+y-7 \sqrt{2}=0\)
4 \(x-y-7 \sqrt{2}=0\)
Straight Line

88672 A square is formed by the lines \(x=0, y=0, x=1\), \(y=1\). Then, the equation of its diagonals will be

1 \(y=x, x+y=2\)
2 \(2 \mathrm{y}=x, x+y=\frac{1}{2}\)
3 \(\mathrm{y}=x, x+y=1\)
4 \(y=2 x, z+y=\frac{1}{4}\)
Straight Line

88673 Find the value of ' \(k\) ' if the angle between the straight lines represented by
\(2 x^{2}+5 x y+3 y^{2}+6 x+7 y+4=0 \text { is } \tan ^{-1}(k) .\)

1 \(\left(\frac{1}{5}\right)\) only
2 \(\left(\frac{-1}{5}\right)\) only
3 \(\pm \frac{1}{5}\)
4 0
Straight Line

88689 A variable line passes through the fixed point \((\alpha, \beta)\) The locus of the foot of the perpendicular from the origin on the line is

1 \(x^{2}+y^{2}-\alpha x-\beta y=0\)
2 \(x^{2}+y^{2}+2 \alpha x+2 \beta y=0\)
3 \(\alpha x+\beta y \pm \sqrt{\left(\alpha^{2}+\beta^{2}\right)}=0\)
4 \(\frac{x^{2}}{\alpha^{2}}+\frac{y^{2}}{\beta^{2}}=1\)
Straight Line

88647 If the midpoint of the section of the straight line intercepted between the axes is \((1,1)\) then the equation of the line is

1 \(2 x+y=3\)
2 \(2 x-y=1\)
3 \(x-y=0\)
4 \(x+y=2\)
Straight Line

88648 The perpendicular distance of a line from the origin is \(7 \mathrm{~cm}\) and its slope is -1 . The equation of line is

1 \(x+y+7 \sqrt{2}=0\)
2 \(x-y+7 \sqrt{2}=0\)
3 \(x+y-7 \sqrt{2}=0\)
4 \(x-y-7 \sqrt{2}=0\)
Straight Line

88672 A square is formed by the lines \(x=0, y=0, x=1\), \(y=1\). Then, the equation of its diagonals will be

1 \(y=x, x+y=2\)
2 \(2 \mathrm{y}=x, x+y=\frac{1}{2}\)
3 \(\mathrm{y}=x, x+y=1\)
4 \(y=2 x, z+y=\frac{1}{4}\)
Straight Line

88673 Find the value of ' \(k\) ' if the angle between the straight lines represented by
\(2 x^{2}+5 x y+3 y^{2}+6 x+7 y+4=0 \text { is } \tan ^{-1}(k) .\)

1 \(\left(\frac{1}{5}\right)\) only
2 \(\left(\frac{-1}{5}\right)\) only
3 \(\pm \frac{1}{5}\)
4 0
Straight Line

88689 A variable line passes through the fixed point \((\alpha, \beta)\) The locus of the foot of the perpendicular from the origin on the line is

1 \(x^{2}+y^{2}-\alpha x-\beta y=0\)
2 \(x^{2}+y^{2}+2 \alpha x+2 \beta y=0\)
3 \(\alpha x+\beta y \pm \sqrt{\left(\alpha^{2}+\beta^{2}\right)}=0\)
4 \(\frac{x^{2}}{\alpha^{2}}+\frac{y^{2}}{\beta^{2}}=1\)
Straight Line

88647 If the midpoint of the section of the straight line intercepted between the axes is \((1,1)\) then the equation of the line is

1 \(2 x+y=3\)
2 \(2 x-y=1\)
3 \(x-y=0\)
4 \(x+y=2\)
Straight Line

88648 The perpendicular distance of a line from the origin is \(7 \mathrm{~cm}\) and its slope is -1 . The equation of line is

1 \(x+y+7 \sqrt{2}=0\)
2 \(x-y+7 \sqrt{2}=0\)
3 \(x+y-7 \sqrt{2}=0\)
4 \(x-y-7 \sqrt{2}=0\)