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

In the given figure, a circle is centred at \((1, 2)\). The diameter of the circle is

If the distance between the points (4, p) and (1, 0) is 5, then p is equal to :

If the points \(A(4, 5)\), \(B(m, 6)\), \(C(4, 3)\) and \(D(1, n)\) taken in this order are the vertices of a parallelogram \(ABCD\), then find the values of \(m\) and \(n\).

The three vertices of a rhombus PQRS are P(2, \(-\)3), Q(6, 5) and R(\(-\)2, 1). Find the coordinates of the fourth vertex S and coordinates of the point where both the diagonals PR and QS intersect.

If \(PQ\) and \(PR\) are tangents to the circle with centre \(O\) and radius \(4 \text{ cm}\) such that \(\angle QPR = 90^{\circ}\), then the length \(OP\) is

\(PQ\) is tangent to a circle with centre \(O\). If \(\angle POR = 65^{\circ}\), then \(m\angle OPR\) is

A circle centred at \((-1, 2)\) passes through the point \((0, 3)\). Radius of the circle is

In the given figure, \(TP\) and \(TQ\) are tangents to a circle with centre \(M\), touching another circle with centre \(N\) at \(A\) and \(B\) respectively. It is given that \(MQ = 13 \text{ cm}\), \(NB = 8 \text{ cm}\), \(BQ = 35 \text{ cm}\) and \(TP = 80 \text{ cm}\).
(i) Name the quadrilateral MQBN. (1)
(ii) Is MN parallel to PA? Justify your answer. (1)
(iii) Find length TB. (1)
(iv) Find length MN. (2)

In the given figure, point D divides the side BC of \(\triangle ABC\) in the ratio \(1 : 2\). Find length AD. (Given coordinates: \(A(1, 5), B(-2, 1), C(4, 2)\))

The line segment joining the points \(P(-4, -2)\) and \(Q(10, 4)\) is divided by y-axis in the ratio

A circle centered at (2, 1) passes through the points A(5, 6) and B(-3, K). Find the value(s) of K. Hence find length of chord AB.

Prove that the point P dividing the line segment joining the points A(-1, 7) and B(4, -3) in the ratio 3 : 2, lies on the line \(x - 3y = -1\). Also find length of PA and PB.

The distance of the point \( A(4a, 3a) \) from x-axis is :

If the points \( A(4, 5), B(m, 6), C(4, 3) \) and \( D(1, n) \) taken in this order are the vertices of a parallelogram ABCD, then find the values of \( m \) and \( n \).

Find the coordinates of the points of trisection of the line segment joining the points \( A(-1, 4) \) and \( B(-3, -2) \).

The mid-point of the line segment joining the points (5, -4) and (6, 4) lies on :

In \(\triangle ABC\), \(DE \parallel BC\). If \(AD = x\), \(DB = x - 2\), \(AE = x + 2\) and \(EC = x - 1\), then find the value of \(x\).

The coordinates of the centre of a circle are \((x - 7, 2x)\). Find the value(s) of ‘x’, if the circle passes through the point \((-9, 11)\) and has radius \(5\sqrt{2}\) units.

Two concentric circles are of radii 5 cm and 4 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Find the ratio in which the x-axis divides the line segment joining the points \((-6, 5)\) and \((-4, -1)\). Also, find the point of intersection.

In the given figure, \(\triangle ABC\) is a right triangle in which \(\angle B = 90^\circ\), \(AB = 4\) cm and \(BC = 3\) cm. Find the radius of the circle inscribed in the triangle ABC.

Prove that : \(PM = \frac{1}{2} (PQ + QR + PR)\)

The mid-point of the line segment joining the points \((5, -4)\) and \((6, 4)\) lies on :

Do the points \(P (1, 0)\), \(Q (- 5, 0)\) and \(R (- 2, 5)\) form a triangle ? If so, name the type of triangle formed.

Find the ratio in which the \(x\)-axis divides the line segment joining the points \((6, 5)\) and \((-4, -1)\). Also find the point of intersection.