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

A line is such that its segment between the straight lines 5x − y − 4 = 0 and 3x + 4y − 4 = 0 is bisected at the point (1, 5). Obtain its equation.

Find the equation of straight line passing through (−2, −7) and having an intercept of length 3 between the straight lines 4x + 3y = 12 and 4x + 3y = 3.

Find the equation of the line passing through the point of intersection of the lines 4x − 7y − 3 = 0 and 2x − 3y + 1 = 0 that has equal intercepts on the axes.

If the straight line \[\frac{x}{a} + \frac{y}{b} = 1\] passes through the point of intersection of the lines x + y = 3 and 2x − 3y = 1 and is parallel to x − y − 6 = 0, find a and b.

Three sides AB, BC and CA of a triangle ABC are 5x − 3y + 2 = 0, x − 3y − 2 = 0 and x + y − 6 = 0 respectively. Find the equation of the altitude through the vertex A.

Find the equation of the line passing through the intersection of the lines 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.

Find the equation of the straight line passing through the point of intersection of the lines 5x − 6y − 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x − 5y + 11 = 0 .

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.