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

Prove that the centres of the three circles x² + y² − 4x − 6y − 12 = 0, x² + y² + 2x + 4y − 10 = 0 and x² + y² − 10x − 16y − 1 = 0 are collinear.

Prove that the radii of the circles x² + y² = 1, x² + y² − 2x − 6y − 6 = 0 and x² + y² − 4x − 12y − 9 = 0 are in A.P.

Find the equation of the circle which passes through the origin and cuts off chords of lengths 4 and 6 on the positive side of the x-axis and y-axis respectively.

Find the equation of the circle concentric with the circle x² + y² − 6x + 12y + 15 = 0 and double of its area.

Find the equation to the circle which passes through the points (1, 1) (2, 2) and whose radius is 1. Show that there are two such circles.

Find the equation of the circle concentric with x² + y² − 4x − 6y − 3 = 0 and which touches the y-axis.

If a circle passes through the point (0, 0),(a, 0),(0, b) then find the coordinates of its centre.

Find the equation of the circle which passes through the points (2, 3) and (4,5) and the centre lies on the straight line y − 4x + 3 = 0.

Find the equation of the circle, the end points of whose diameter are (2, −3) and (−2, 4). Find its centre and radius.

Find the equation of the circle the end points of whose diameter are the centres of the circles x² + y² + 6x − 14y − 1 = 0 and x² + y² − 4x + 10y − 2 = 0.

The sides of a square are x = 6, x = 9, y = 3 and y = 6. Find the equation of a circle drawn on the diagonal of the square as its diameter.

Find the equation of the circle circumscribing the rectangle whose sides are x − 3y = 4, 3x + y = 22, x − 3y = 14 and 3x + y = 62.

Find the equation of the circle passing through the origin and the points where the line 3x + 4y = 12 meets the axes of coordinates.

Find the equation of the circle which passes through the origin and cuts off intercepts aand b respectively from x and y - axes.

The abscissae of the two points A and B are the roots of the equation x² + 2ax − b² = 0 and their ordinates are the roots of the equation x² + 2px − q² = 0. Find the equation of the circle with AB as diameter. Also, find its radius.

ABCD is a square whose side is a; taking AB and AD as axes, prove that the equation of the circle circumscribing the square is x² + y² − a (x + y) = 0.