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

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola 

x² + y = 6x − 14

For the parabola y² = 4px find the extremities of a double ordinate of length 8 p. Prove that the lines from the vertex to its extremities are at right angles. 

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.  

Write the axis of symmetry of the parabola y² = x. 

Write the distance between the vertex and focus of the parabola y² + 6y + 2x + 5 = 0. 

Write the length of the chord of the parabola y² = 4ax which passes through the vertex and is inclined to the axis at \[\frac{\pi}{4}\] 

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.