Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions for Mathematics

Find the distance between parallel lines:

15x + 8y – 34 = 0 and 15x + 8y + 31 = 0

Find the distance between parallel lines  l (x + y) + p = 0 and l (x + y) – r = 0

What are the points on the y-axis whose distance from the line  `x/3 + y/4 = 1` is 4 units.

Find perpendicular distance from the origin to the line joining the points (cosΘ, sin Θ) and (cosΦ, sin Φ).

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 may be at a distance of 3 units from this point.

If sum of the perpendicular distances of a variable point P (x, y) from the lines x + y – 5 = 0 and 3x – 2y+ 7 = 0 is always 10. Show that P must move on a line.

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.

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum.

x² = 6y

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum.

y² = – 8x

Find the equation of the parabola that satisfies the following condition:

Vertex (0, 0) passing through (2, 3) and axis is along x-axis

Find the equation of the parabola that satisfies the following condition:

Vertex (0, 0), passing through (5, 2) and symmetric with respect to y-axis.

An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?