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

Find the points on the line x + y = 4 which lie at a unit distance from the line 4x + 3y = 10.

If the sum of the distances of a moving point in a plane from the axes is 1, then find the locus of the point.

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 ______.

The distance between the lines y = mx + c₁ and y = mx + c₂ is ______.

A point equidistant from the lines 4x + 3y + 10 = 0, 5x – 12y + 26 = 0 and 7x + 24y – 50 = 0 is ______.

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 ______.

A point moves so that square of its distance from the point (3, –2) is numerically equal to its distance from the line 5x – 12y = 3. The equation of its locus is ______.

The value of the λ, if the lines (2x + 3y + 4) + λ (6x – y + 12) = 0 are

An equilateral triangle is inscribed in the parabola y² = 4ax whose one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

The equations of the lines joining the vertex of the parabola y² = 6x to the points on it which have abscissa 24 are ______.

The equation of the parabola whose focus is the point (2, 3) and directrix is the line x – 4y + 3 = 0 is ______.

Find the coordinates of a point on the parabola y² = 8x whose focal distance is 4.

Find the length of the line segment joining the vertex of the parabola y² = 4ax and a point on the parabola where the line segment makes an angle θ to the x-axis.

If the points (0, 4) and (0, 2) are respectively the vertex and focus of a parabola, then find the equation of the parabola.

If the line y = mx + 1 is tangent to the parabola y² = 4x then find the value of m.

Find the equation of the following parabolas:

Directrix x = 0, focus at (6, 0)

Find the equation of the following parabolas:

Vertex at (0, 4), focus at (0, 2)

Find the equation of the following parabolas:

Focus at (–1, –2), directrix x – 2y + 3 = 0

Find the equation of the set of all points the sum of whose distances from the points (3, 0) and (9, 0) is 12.

Find the equation of the set of all points whose distance from (0, 4) are `2/3` of their distance from the line y = 9.