List of top Mathematics Questions on Various Forms of the Equation of a Line

Let $O$ be the origin and $P$ be a point on a line such that $OP$ is perpendicular to that line. If $OP$ makes an obtuse angle $\alpha$ with the $x$-axis, $OP = 5$ and $\sin \alpha = \frac{3}{5}$, then the equation of the line is

Let O be the origin and let P be a point on the line \(x + \sqrt{3}y = 10\). If OP is perpendicular to the line, then the angle between OP and the y-axis is

If $a y = x + b$ is the equation of the line passing through the points (-5, -2) and (4, 7), then the value of $2a + b$ is equal to:

Which one of the following lines passes through the point of intersection of $x+y=5$ and $2x+y=7$? ________.

Let \( [x] \) denote the greatest integer less than or equal to \( x \). Then the domain of \( f(x) = \sec^{-1} (2[x] + 1) \) is:

Let the coefficients of three consecutive terms \( T_r \), \( T_{r+1} \), and \( T_{r+2} \) in the binomial expansion of \( (a + b)^{12} \) be in a G.P. and let \( p \) be the number of all possible values of \( r \). Let \( q \) be the sum of all rational terms in the binomial expansion of \( \left( 4\sqrt{3} + 3\sqrt{4} \right)^{12} \). Then \( p + q \) is equal to:

If \( y = y(x) \) is the solution of the differential equation, \[ \sqrt{4 - x^2} \frac{dy}{dx} = \left( \left( \sin^{-1} \left( \frac{x}{2} \right) \right)^2 - y \right) \sin^{-1} \left( \frac{x}{2} \right), \] where \( -2 \leq x \leq 2 \), and \( y(2) = \frac{\pi^2 - 8}{4} \), then \( y^2(0) \) is equal to:

The equation of line, where length of the perpendicular segment from origin to the line is 4 and the inclination of this perpendicular segment with the positive direction of X-axis is $30^\circ$, is

The equation of a line passing through $(p \cos \alpha, p \sin \alpha)$ and making an angle $(90 + \alpha)$ with positive direction of X-axis is

The x-intercept of a line passing through the points $\left(-\frac{1}{2}, 1\right)$ and $(1, 2)$ is :

If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ intersect, then the value of $k$ is

The parametric equations of a line passing through the points $A(3,4,-7)$ and $B(1,-1,6)$ are

The equation of a line passing through $(p \cos \alpha, p \sin \alpha)$ and making an angle $(90 + \alpha)$ with positive direction of X-axis is

Find the equation of the line which passes through the points (-1, 1) and (2, -4).

The perpendicular from the origin to a line meets it at the point (–2, 9), find the equation of the line.

The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L= 125.134 when C = 110, express L in terms of C.

The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs 17/litre?

P (a,b) is the mid-point of a line segment between axes. Show that equation of the line is \(\frac{x}{a}+\frac{y}{b}=2\)

Point R (h, k) divides a line segment between the axes in the ratio 1: 2. Find equation of the line.

By using the concept of equation of a line, prove that the three points (3, 0), (– 2, – 2) and (8, 2) are collinear.

If three point (h, 0), (a, b) and (0, k) lie on a line, show that \(\frac ah+ \frac bk=1\).