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

Find the equation of a line passing through the point (2, 3) and parallel to the line 3x − 4y + 5 = 0.

Find the equation of the straight line perpendicular to 5x − 2y = 8 and which passes through the mid-point of the line segment joining (2, 3) and (4, 5).

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse: 

x² + 2y² − 2x + 12y + 10 = 0 

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse: 

 x² + 4y² − 4x + 24y + 31 = 0 

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse: 

4x² + y² − 8x + 2y + 1 = 0 

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse: 

3x² + 4y² − 12x − 8y + 4 = 0 

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse: 

4x² + 16y² − 24x − 32y − 12 = 0 

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:

x² + 4y² − 2x = 0 

Find the equation of an ellipse whose foci are at (± 3, 0) and which passes through (4, 1).

Find the equation of a line drawn perpendicular to the line \[\frac{x}{4} + \frac{y}{6} = 1\] through the point where it meets the y-axis.

A rod of length 12 m moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with x-axis. 

Find the equation of the set of all points whose distances from (0, 4) are\[\frac{2}{3}\] of their distances from the line y = 9. 

The line 2x + 3y = 12 meets the x-axis at A and y-axis at B. The line through (5, 5) perpendicular to AB meets the x-axis and the line AB at C and E respectively. If O is the origin of coordinates, find the area of figure OCEB.

If the lengths of semi-major and semi-minor axes of an ellipse are 2 and \[\sqrt{3}\] and their corresponding equations are y − 5 = 0 and x + 3 = 0, then write the equation of the ellipse. 

Write the eccentricity of the ellipse 9x² + 5y² − 18x − 2y − 16 = 0. 

PSQ is a focal chord of the ellipse 4x² + 9y² = 36 such that SP = 4. If S' is the another focus, write the value of S'Q. 

If S and S' are two foci of the ellipse \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] and B is an end of the minor axis such that ∆BSS' is equilateral, then write the eccentricity of the ellipse.

If the minor axis of an ellipse subtends an equilateral triangle with vertex at one end of major axis, then write the eccentricity of the ellipse.