A line cutting off intercept \(-3\) from the y-axis and the tangent of angle to the x-axis is \(\tfrac{3}{?}\), its equation is
5y - 3x + 15 = 0
3y - 5x + 15 = 0
5y - 3x - 15 = 0
None of these
Slope of a line which cuts off intercepts of equal lengths on the axes is
-1
0
2
\(\sqrt{3}\)
The equation of the straight line passing through the point \((3,2)\) and perpendicular to the line \(y = x\) is
x - y = 5
x + y = 5
x + y = 1
x - y = 1
The equation of the line passing through the point \((1,2)\) and perpendicular to the line \(x + y + 1 = 0\) is
y - x + 1 = 0
y - x - 1 = 0
y - x + 2 = 0
y - x - 2 = 0
The tangent of angle between the lines whose intercepts on the axes are \(a, -b\) and \(b, -a\), respectively, is
\(\dfrac{a^2 - b^2}{ab}\)
\(\dfrac{b^2 - a^2}{2}\)
\(\dfrac{b^2 - a^2}{2ab}\)
None of these
If the line \(\dfrac{x}{a} + \dfrac{y}{b} = 1\) passes through the points \((2,-3)\) and \((4,-5)\), then \((a,b)\) is
(1, 1)
(-1, 1)
(1, -1)
(-1, -1)
The distance of the point of intersection of the lines \(2x - 3y + 5 = 0\) and \(3x + 4y = 0\) from the line \(5x - 2y = 0\) is
\(\dfrac{130}{17\sqrt{29}}\)
\(\dfrac{13}{7\sqrt{29}}\)
\(\dfrac{130}{7}\)
None of these
The equations of the lines which pass through the point \((3,-2)\) and are inclined at \(60^\circ\) to the line \(\sqrt{3}\,x + y = 1\) is
\(y + 2 = 0\) and \(\sqrt{3}x - y - 2 - 3\sqrt{3} = 0\)
\(x - 2 = 0\) and \(\sqrt{3}x - y + 2 + 3\sqrt{3} = 0\)
\(\sqrt{3}x - y - 2 - 3\sqrt{3} = 0\)
None of these
The equations of the lines passing through the point \((1,0)\) and at a distance \(\dfrac{\sqrt{3}}{2}\) from the origin are
\(\sqrt{3}x + y - \sqrt{3} = 0\), \(\sqrt{3}x - y - \sqrt{3} = 0\)
\(\sqrt{3}x + y + \sqrt{3} = 0\), \(\sqrt{3}x - y + \sqrt{3} = 0\)
x + \sqrt{3}y - \sqrt{3} = 0, \; x - \sqrt{3}y - \sqrt{3} = 0
None of these
The distance between the lines \(y = mx + c_1\) and \(y = mx + c_2\) is
\(\dfrac{c_1 - c_2}{\sqrt{m^2 + 1}}\)
\(\dfrac{|c_1 - c_2|}{\sqrt{1 + m^2}}\)
\(\dfrac{c_2 - c_1}{\sqrt{1 + m^2}}\)
0
The coordinates of the foot of perpendiculars from the point \((2,3)\) on the line \(y = 3x + 4\) is given by
\(\left(\dfrac{37}{10}, -\dfrac{1}{10}\right)\)
\(\left(-\dfrac{1}{10}, \dfrac{37}{10}\right)\)
\(\left(\dfrac{10}{37}, -10\right)\)
\(\dfrac{2}{3}, -\dfrac{1}{3}\)
If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is \((3,2)\), then the equation of the line will be
2x + 3y = 12
3x + 2y = 12
4x - 3y = 6
5x - 2y = 10
Equation of the line passing through \((1,2)\) and parallel to the line \(y = 3x - 1\) is
y + 2 = x + 1
y + 2 = 3(x + 1)
y - 2 = 3(x - 1)
y - 2 = x - 1
Equations of diagonals of the square formed by the lines \(x = 0\), \(y = 0\), \(x = 1\) and \(y = 1\) are
y = x, \; y + x = 1
y = x, \; x + y = 2
2y = x, \; y + x = \dfrac{1}{3}
y = 2x, \; y + 2x = 1
For specifying a straight line, how many geometrical parameters should be known?
1
2
4
3
The point \((4,1)\) undergoes the following two successive transformations:
(i) Reflection about the line \(y = x\)
(ii) Translation through a distance 2 units along the positive x-axis
Then the final coordinates of the point are
(4, 3)
(3, 4)
(1, 4)
\(\left(\tfrac{7}{2},\tfrac{7}{2}\right)\)
A point equidistant from the lines \(4x + 3y + 10 = 0\), \(5x - 12y + 26 = 0\) and \(7x + 24y - 50 = 0\) is
(1, -1)
(1, 1)
(0, 0)
(0, 1)
A line passes through \((2,2)\) and is perpendicular to the line \(3x + y = 3\). Its y-intercept is
\(\dfrac{1}{3}\)
\(\dfrac{2}{3}\)
1
\(\dfrac{4}{3}\)
The ratio in which the line \(3x + 4y + 2 = 0\) divides the distance between the lines \(3x + 4y + 5 = 0\) and \(3x + 4y - 5 = 0\) is
1 : 2
3 : 7
2 : 3
2 : 5
One vertex of the equilateral triangle with centroid at the origin and one side as \(x + y - 2 = 0\) is
(-1, -1)
(2, 2)
(-2, -2)
(2, -2)