Circle Questions

Two circles x2 + y2 = 6 and x2 + y2 - 6x + 8 = 0 Then the equation of the circle through their points of intersection and point (1, 1) is...

If the two circles (x -1)2 + ( y - 3)2 = r2 and x2 + y2 -8x + 2y + 8 = 0 intersect in two distinct points. then

Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and touching the circle C externally, then the radius of T is equal to...

The common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is...

If are four distinct points on a circle of radius 4 units then, abcd =

The x coordinates of two points A and B are roots of equation x2 + 2x − a2 = 0 and y coordinate are roots of equation y2 + 4y − b2 = 0 then equation of the circle which has diameter AB is-...

Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B an...

Let the orthocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is:...

If the tangent at (1, 7) to the curve x2 = y - 6 touches the circle x2 + y2 + 16x + 12y + c = 0 then the value of c is :

Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length or y-axis is (are)

A circle S passes through the point (0, 1) and is orthogonal to the circles (x - 1)2 + y2 = 16 and x2 + y2 = 1. Then

For the equation x2 + y2 + 2λx + 4 = 0 which of the following can be true -

If latus rectum of an ellipse = 1 {0 < b < 4}, subtend angle 2θ at farthest vertex such that cosec θ = √5, then -...

If (5, 12) and (24, 7) are the foci of a conic passing through the origin, then the eccentricity of conic is -

Tangent to the parabola y2 = 4ax at point P meets the tangent at vertex A, at point B and the axis of parabola at T. Q is any point on this tangent and N is the foot of perpendicular from Q on SP, whe...

Consider the hyperbola H : x2 − y2 = 1 and a circle S with center N(x2, 0). Suppose that H and S touch each other at a point P(x1, y1) with x1 > 1 and y1 > 0. The common tangent to H and S...

Let P and Q be distinct points on the parabola y2 = 2x such that a circle with PQ as diameter passesthrough the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle &...

Consider the family of all circles whose centers lie on the straight line y = x. If this family of circles is represented by the differential equation Py″ + Qy′ + 1 = 0, where P,Q are func...

If a chord, which is not a tangent, of the parabola y2 = 16x has the equation 2x + y = p, and midpoint (h, k), then which of the following is(are) possible value(s) of p, h and k ?...

In a triangle PQR, let ∠PQR = 30° and the sides PQ and QR have lengths 10 3 and 10, respectively. Then, which of the following statement(s) is (are) TRUE ?...