NCERT Solutions
Class 11 - Mathematics - Chapter 9: STRAIGHT LINES

Miscellaneous Exercise on Chapter 9

Find the values of \(k\) for which the line \((k-3)x - (4-k^2)y + k^2 - 7k + 6 = 0\) is:

(a) parallel to the x-axis,
(b) parallel to the y-axis,
(c) passing through the origin.

Find the equations of the lines which cut off intercepts on the axes whose sum and product are 1 and −6 respectively.

What are the points on the y-axis whose distance from the line \(\dfrac{x}{3} + \dfrac{y}{4} = 1\) is 4 units?

Find perpendicular distance from the origin to the line joining the points \((\cos\theta, \sin\theta)\) and \((\cos\phi, \sin\phi)\).

Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines \(x - 7y + 5 = 0\) and \(3x + y = 0\).

Find the equation of a line drawn perpendicular to the line \(\dfrac{x}{4} + \dfrac{y}{6} = 1\) through the point where it meets the y-axis.

Find the area of the triangle formed by the lines \(y - x = 0\), \(x + y = 0\) and \(x - k = 0\).

Find the value of \(p\) so that the three lines \(3x + y - 2 = 0\), \(px + 2y - 3 = 0\) and \(2x - y - 3 = 0\) may intersect at one point.

Find the equation of the lines through the point \((3,2)\) which make an angle of 45° with the line \(x - 2y = 3\).

Find the equation of the line passing through the point of intersection of the lines \(4x + 7y - 3 = 0\) and \(2x - 3y + 1 = 0\) that has equal intercepts on the axes.

Find the equation of the right bisector of the line segment joining the points \((3,4)\) and \((-1,2)\).

In what ratio is the line joining \((-1,1)\) and \((5,7)\) divided by the line \(x + y = 4\)?

Find the distance of the line \(4x + 7y + 5 = 0\) from the point \((1,2)\) along the line \(2x - y = 0\).

Find the direction in which a straight line must be drawn through the point \((-1,2)\) so that its point of intersection with the line \(x + y = 4\) is at a distance of 3 units from this point.

The hypotenuse of a right-angled triangle has its ends at \((1,3)\) and \((-4,1)\). Find the equations of the legs of the triangle which are parallel to the axes.

Find the image of the point \((3,8)\) with respect to the line \(x + 3y = 7\) assuming the line to be a plane mirror.

If the lines \(y = 3x + 1\) and \(2y = x + 3\) are equally inclined to the line \(y = mx + 4\), find the value of \(m\).

Find the equation of the line which is equidistant from the parallel lines \(9x + 6y - 7 = 0\) and \(3x + 2y + 6 = 0\).

A ray of light passing through the point \((1,2)\) reflects on the x-axis at point A and the reflected ray passes through the point \((5,3)\). Find the coordinates of A.

A person standing at the junction of two straight paths represented by \(2x - 3y + 4 = 0\) and \(3x + 4y - 5 = 0\) wants to reach the path whose equation is \(6x - 7y + 8 = 0\) in the least time. Find the equation of the path that he should follow.