Science (English Medium) कक्षा ११ - CBSE Question Bank Solutions

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. 

If a latus rectum of an ellipse subtends a right angle at the centre of the ellipse, then write the eccentricity of the ellipse. 

Find the length of the perpendicular from the origin to the straight line joining the two points whose coordinates are (a cos α, a sin α) and (a cos β, a sin  β).

Find the length of the perpendicular from the point (4, −7) to the line joining the origin and the point of intersection of the lines 2x − 3y + 14 = 0 and 5x + 4y − 7 = 0.

Find the distance of the point (1, 2) from the straight line with slope 5 and passing through the point of intersection of x + 2y = 5 and x − 3y = 7.

Find the equation of the straight lines passing through the origin and making an angle of 45° with the straight line \[\sqrt{3}x + y = 11\].