Arts (English Medium) Class 11 - CBSE Question Bank Solutions

The reflection of the point (4, – 13) about the line 5x + y + 6 = 0 is ______.

Find the equation of the line passing through the point (5, 2) and perpendicular to the line joining the points (2, 3) and (3, – 1).

Find the angle between the lines y = `(2 - sqrt(3)) (x + 5)` and y = `(2 + sqrt(3))(x - 7)`

Show that the tangent of an angle between the lines `x/a + y/b` = 1 and `x/a - y/b` = 1 is `(2ab)/(a^2 - b^2)`

Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120° with the positive direction of x-axis.

Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2).

If the equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, – 1), then find the length of the side of the triangle.

A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2, 0), (0, 2) and (1, 1) on the line is zero. Find the coordinates of the point P.

P₁, P2 are points on either of the two lines `- sqrt(3) |x|` = 2 at a distance of 5 units from their point of intersection. Find the coordinates of the foot of perpendiculars drawn from P₁, P₂ on the bisector of the angle between the given lines.

If p is the length of perpendicular from the origin on the line `x/a + y/b` = 1 and a², p², b² are in A.P, then show that a⁴ + b⁴ = 0.

Slope of a line which cuts off intercepts of equal lengths on the axes is ______.

The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is ______.

The tangent of angle between the lines whose intercepts on the axes are a, – b and b, – a, respectively, is ______.

The coordinates of the foot of perpendiculars from the point (2, 3) on the line y = 3x + 4 is given by ______.

Equation of the line passing through (1, 2) and parallel to the line y = 3x – 1 is ______.

Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are ______.

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 ______.

One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is ______.

Equations of the lines through the point (3, 2) and making an angle of 45° with the line x – 2y = 3 are ______.

The points (3, 4) and (2, – 6) are situated on the ______ of the line 3x – 4y – 8 = 0.