List of top Mathematics Questions on Coordinate Geometry asked in UK Class X

In figure \( AB = 8 \, \text{cm} \) and \( PE = 3 \, \text{cm} \), then find AE. 

Prove that the parallelogram circumscribing a circle is a rhombus.
A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it possible to do so? If yes, at what distances from the two gates should the pole be erected?
Find a point on the Y-axis which is equidistant from the points \( A(6, 5) \) and \( B(-4, 3) \).
Find the coordinates of the points that trisect the line segment AB joining the points \( A(-1, 2) \) and \( B(2, 8) \).
Assertion (A): The tangent to a circle is a special case of the secant, when the two end points of its corresponding chord coincide.
Reason (R): A tangent to a circle is a line that intersects the circle at only one point.
If the mid point of a line segment joining the points \( (h, 3) \) and \( (6, 5) \) is \( (4, 4) \), then find the value of h.
The distance of the point \(P(-6, 8)\) from the origin is:
In \( \triangle ABC \), \( DE \parallel BC \) such that \( \frac{AD}{DB} = \frac{3}{5} \); if \( AC = 5.6 \, \text{cm} \), then \( AE \) is equal to:
Which of the following pairs of lines in a circle cannot be parallel: