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

Express the following as the sum or difference of sines and cosines:
 2 cos 7x cos 3x

At what point of the parabola x² = 9y is the abscissa three times that of ordinate? 

Find the equation of a parabola with vertex at the origin, the axis along x-axis and passing through (2, 3).

Find the equation of a parabola with vertex at the origin and the directrix, y = 2. 

Find the equation of the parabola whose focus is (5, 2) and having vertex at (3, 2). 

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest wire being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle. 

Find the equations of the lines joining the vertex of the parabola y² = 6x to the point on it which have abscissa 24. 

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

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. 

Write the equation of the directrix of the parabola x² − 4x − 8y + 12 = 0. 

Write the equation of the parabola with focus (0, 0) and directrix x + y − 4 = 0.

PSQ is a focal chord of the parabola y² = 8x. If SP = 6, then write SQ. 

Write the equation of the parabola whose vertex is at (−3,0) and the directrix is x + 5 = 0. 

The equation of the parabola whose vertex is (a, 0) and the directrix has the equation x + y = 3a, is 

The parametric equations of a parabola are x = t² + 1, y = 2t + 1. The cartesian equation of its directrix is 

The line 2x − y + 4 = 0 cuts the parabola y² = 8x in P and Q. The mid-point of PQ is

The equation 16x² + y² + 8xy − 74x − 78y + 212 = 0 represents 

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

The locus of the points of trisection of the double ordinates of a parabola is a