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

If the coordinates of the vertex and focus of a parabola are (−1, 1) and (2, 3) respectively, then write the equation of its directrix. 

In the parabola y² = 4ax, the length of the chord passing through the vertex and inclined to the axis at π/4 is

The directrix of the parabola x² − 4x − 8y + 12 = 0 is

The equation of the parabola with focus (0, 0) and directrix x + y = 4 is 

The vertex of the parabola (y − 2)² = 16 (x − 1) is 

Find the equation of the line parallel to x-axis and having intercept − 2 on y-axis.

Draw the lines x = − 3, x = 2, y = − 2, y = 3 and write the coordinates of the vertices of the square so formed.

Find the equations of the straight lines which pass through (4, 3) and are respectively parallel and perpendicular to the x-axis.

Find the equation of the straight line passing through (−2, 3) and inclined at an angle of 45° with the x-axis.

Find the equation of the line passing through (0, 0) with slope m.

Find the equation of the line passing through \[(2, 2\sqrt{3})\] and inclined with x-axis at an angle of 75°.

Find the equation of the straight line which passes through the point (1,2) and makes such an angle with the positive direction of x-axis whose sine is \[\frac{3}{5}\].

Find the equation of the straight line passing through (3, −2) and making an angle of 60° with the positive direction of y-axis.

Find the equation of the straight line which divides the join of the points (2, 3) and (−5, 8) in the ratio 3 : 4 and is also perpendicular to it.

Prove that the perpendicular drawn from the point (4, 1) on the join of (2, −1) and (6, 5) divides it in the ratio 5 : 8.

Find the equations to the altitudes of the triangle whose angular points are A (2, −2), B (1, 1) and C (−1, 0).