List of top Mathematics & Statistics Questions on Co-ordinate Geometry

If \( A(5, 1, p) \), \( B(1, q, p) \), and \( C(1, -2, 3) \) are vertices of a triangle and \( G \left( -\frac{4}{3}, \frac{1}{3}, -\frac{4}{3} \right) \) is its centroid, then find the values of \( p \), \( q \) by vector method.
If angle between the lines represented by \( ax^2 + 2hxy + by^2 = 0 \) is equal to the angle between the lines represented by \( 2x^2 - 5xy + 3y^2 = 0 \), then show that \( 100 (h^2 - ab) = (a + b)^2 \).
Find the cartesian equation of the plane passing through \( A(1, 2, 3) \) and the direction ratios of whose normal are 3, 2, 5.
Find the value of \( k \), if \( 2x + y = 0 \) is one of the lines represented by \( 3x^2 + kxy + 2y^2 = 0 \)
Write the separate equations of lines represented by the equation \( x^2 - 9y^2 = 0 \)
Equation of line passing through the points (0, 0, 0) and (2, 1, -3) is
Find the distance between the parallel lines \( \frac{x}{2} = \frac{y}{-1} = \frac{z}{2} \) and \( \frac{x-1}{2} = \frac{y+1}{-1} = \frac{z-4}{2} \).
Find the cartesian coordinates of the point whose polar coordinates are \( \left( \frac{1}{2}, \frac{\pi}{3} \right) \).