List of top Mathematics Questions on Coordinate Geometry asked in Maharashtra Class XII

If \( \theta \) is the acute angle between the lines represented by \( ax^2 + 2hxy + by^2 = 0 \), then prove that \( \tan \theta = \frac{2 \sqrt{h^2 - ab}}{a + b} \).
Find the cartesian coordinates of the point whose polar coordinates are \( \left( 2, \frac{\pi}{4} \right) \).
If \( ax^2 + 2hxy + by^2 = 0 \) represents a pair of lines and \( h^2 = ab \neq 0 \), then find the ratio of their slopes.
Write the joint equation of co-ordinate axes.
The area of the triangle with vertices (1, 2, 0), (1, 0, 2), and (0, 3, 1) in sq. unit is _______.