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

If the line y = \[\sqrt{3}\] x + k touches the circle x² + y² = 16, then find the value of k. 

Show that the point (x, y) given by  \[x = \frac{2at}{1 + t^2}\] and \[y = a\left( \frac{1 - t^2}{1 + t^2} \right)\]  lies on a circle for all real values of t such that \[- 1 \leq t \leq 1\] where a is any given real number.

The circle x² + y² − 2x − 2y + 1 = 0 is rolled along the positive direction of x-axis and makes one complete roll. Find its equation in new-position.

Find the coordinates of the centre and radius of each of the following circles:  x² + y² + 6x − 8y − 24 = 0

Find the coordinates of the centre and radius of each of the following circles: 2x² + 2y² − 3x + 5y = 7

Find the coordinates of the centre and radius of the following circle:

1/2 (x² + y²) + x cos θ + y sin θ − 4 = 0

Find the coordinates of the centre and radius of each of the following circles:  x² + y² − ax − by = 0

Find the equation of the circle passing through the points:

(5, 7), (8, 1) and (1, 3)

Find the equation of the circle passing through the points:

 (5, −8), (−2, 9) and (2, 1)

Find the equation of the circle passing through the points:

 (0, 0), (−2, 1) and (−3, 2)

Find the equation of the circle which circumscribes the triangle formed by the lines x + y + 3 = 0, x − y + 1 = 0 and x = 3