List of top Mathematics Questions on Circles asked in CBSE CLASS XII

Roundabouts are often made on busy roads to ease the traffic and avoid red lights.
One such round-about is made such that the equation representing its boundary is given by \( C_1 : x^2 + y^2 = 64 \). There is a circular pond with a fountain in the middle of the roundabout whose equation is given by \( C_2 : x^2 + y^2 = 4 \). Based on the given information
If the radius of a circle is increasing at the rate of 0.5 cm/s, then the rate of increase of its circumference is:
The vertices of triangle \( \triangle ABC \) are \( A(1, 1, 0), B(1, 2, 1) \), and \( C(-2, 2, -1) \). Find the equations of the medians through A and B. Use the equations so obtained to find the coordinates of the centroid.

Assertion (A): A line in space cannot be drawn perpendicular to \( x \), \( y \), and \( z \) axes simultaneously. 
Reason (R): For any line making angles \( \alpha, \beta, \gamma \) with the positive directions of \( x \), \( y \), and \( z \) axes respectively, \[ \cos^2\alpha + \cos^2\beta + \cos^2\gamma = 1. \]

The position vectors of vertices of \( \Delta ABC \) are \( A(2\hat{i} - \hat{j} + \hat{k}) \), \( B(\hat{i} - 3\hat{j} - 5\hat{k}) \), and \( C(3\hat{i} - 4\hat{j} - 4\hat{k}) \). Find all the angles of \( \Delta ABC \).
Direction ratios of a vector parallel to the line \( \frac{x - 1}{2} = -y = \frac{2z + 1}{6} \) are:
Find the equation of the line which bisects the line segment joining points \( A(2, 3, 4) \) and \( B(4, 5, 8) \) and is perpendicular to the lines: \[ \frac{x - 8}{3} = \frac{y + 19}{-16} = \frac{z - 10}{7} \quad \text{and} \quad \frac{x - 15}{3} = \frac{y - 29}{8} = \frac{z - 5}{-5}. \]
The position vectors of vertices of \( \Delta ABC \) are \( A(2\hat{i} - \hat{j} + \hat{k}) \), \( B(\hat{i} - 3\hat{j} - 5\hat{k}) \), and \( C(3\hat{i} - 4\hat{j} - 4\hat{k}) \). Find all the angles of \( \Delta ABC \).
Direction ratios of a vector parallel to the line \( \frac{x - 1}{2} = -y = \frac{2z + 1}{6} \) are:
Find the equation of a line \( l_2 \) which is the mirror image of the line \( l_1 \) with respect to line \( l : \frac{x}{1} = \frac{y - 1}{2} = \frac{z - 2}{3} \), given that line \( l_1 \) passes through the point \( P(1, 6, 3) \) and is parallel to line \( l \).
If the direction cosines of a line are \( \sqrt{3}k, \sqrt{3}k, \sqrt{3}k \), then the value of \( k \) is:
The distance of point \( P(a, b, c) \) from the y-axis is: