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

Show that the following statement is true
"The integer n is even if an only if n² is even"

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

y² = 8x 

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

4x² + y = 0 

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

y² − 4y − 3x + 1 = 0 

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

y² − 4y + 4x = 0 

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

 y² + 4x + 4y − 3 = 0 

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

y² = 8x + 8y 

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

y² = 8x + 8y

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

 4 (y − 1)² = − 7 (x − 3) 

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

 y² = 5x − 4y − 9 

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