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

Find the equation of the right bisector of the line segment joining the points \( (3,4) \) and \( (1,2) \).

The vertices of \( \triangle PQR \) are \( P(2,1) \), \( Q(-2,3) \), and \( R(4,5) \). Find the equation of the median through the vertex \( R \).

Find the coordinates of the focus, axis of the parabola, the equation of the directrix, and the length of the latus rectum, if \( y^2 = 12x \).

Find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity, and the length of the latus rectum of the ellipse: \[ \frac{x^2}{36} + \frac{y^2}{16} = 1 \]

Show that the points (-2, 3, 5), (1, 2, 3), and (7, 0, -1) are collinear OR verify that the points (0,7,10), (-1,6,6) and (-4,9,6) are the vertices of a right angled triangle.

Verify that (0,7,10), (-1,6,6) and (-4,9,6) are the vertices of a right angled triangle.

Assertion (A): The radius of a circle in which a central angle of 60 degrees intercepts an arc length of 37.4 cm (using \( \pi = \frac{22}{7} \))
Reason (R): The formula to calculate the length of an arc is \( l = Q \times r \), where \( l \) is the arc length, \( Q \) is the central angle in radians, and \( r \) is the radius of the circle.