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

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 \[\sqrt{3}x + y = 11\].

Find the equations to the straight lines which pass through the origin and are inclined at an angle of 75° to the straight line \[x + y + \sqrt{3}\left( y - x \right) = a\].

Find the equations of the straight lines passing through (2, −1) and making an angle of 45° with the line 6x + 5y − 8 = 0.

Find the equations to the straight lines which pass through the point (h, k) and are inclined at angle tan⁻¹ m to the straight line y = mx + c.

Find the equations to the straight lines passing through the point (2, 3) and inclined at and angle of 45° to the line 3x + y − 5 = 0.

Find the equations to the sides of an isosceles right angled triangle the equation of whose hypotenues is 3x + 4y = 4 and the opposite vertex is the point (2, 2).

The equation of one side of an equilateral triangle is x − y = 0 and one vertex is \[(2 + \sqrt{3}, 5)\]. Prove that a second side is \[y + (2 - \sqrt{3}) x = 6\]  and find the equation of the third side.

Find the equations of the two straight lines through (1, 2) forming two sides of a square of which 4x+ 7y = 12 is one diagonal.

Find the equations of two straight lines passing through (1, 2) and making an angle of 60° with the line x + y = 0. Find also the area of the triangle formed by the three lines.