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

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.

If the vertices of a triangle have integral coordinates, then the triangle can not be equilateral.

The points A(– 2, 1), B(0, 5), C(– 1, 2) are collinear.

The vertex of an equilateral triangle is (2, 3) and the equation of the opposite side is x + y = 2. Then the other two sides are y – 3 = `(2 +- sqrt(3)) (x - 2)`.

The line `x/a + y/b` = 1 moves in such a way that `1/a^2 + 1/b^2 = 1/c^2`, where c is a constant. The locus of the foot of the perpendicular from the origin on the given line is x² + y² = c².

Line joining the points (3, – 4) and (– 2, 6) is perpendicular to the line joining the points (–3, 6) and (9, –18).

The equation of the line through the intersection of the lines 2x – 3y = 0 and 4x – 5y = 2 and

Find the equation of the circle which touches the both axes in first quadrant and whose radius is a.