Circle Equation & Properties: JEE Questions & Solutions

Let PQ and MN be two straight lines touching the circle x^2+y^2-4x-6y-3=0 at the points A and B respectively. Let O be the centre of the…

If P is a point on the circle x^2 + y^2 = 4, Q is a point on the straight line 5x + y + 2 = 0 and x - y + 1 = 0 is the perpendicular…

Let the set of all values of r, for which the circles (x + 1)^2 + (y + 4)^2 = r^2 and x^2 + y^2 - 4x - 2y - 4 = 0 intersect at two distinct…

Let a circle of radius 4 pass through the origin O, the points A(- 3a,0) and B(0,- 2b), where a and b are real parameters and ab 0. Then…

Let y = x be the equation of a chord of the circle C1 (in the closed half-plane x 0) of diameter 10 passing through the origin. Let C2 be…

Let the circle x^2+y^2=4 intersect the x-axis at points A(a,0) and B(b,0). Let P(2,2), 0< < 2, and Q(2,2) be two points on the circle such…

A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has centre at…

Let circle C be the image of x^2 + y^2 - 2x + 4y - 4 = 0 in the line 2x - 3y + 5 = 0 and A be the point on C such that OA is parallel to…

Let the equation of the circle, which touches x-axis at the point (a, 0) and cuts off an intercept of length b on y-axis be x^2 + y^2 - cx…

Let the line x + y = 1 meet the circle x^2 + y^2 = 4 at the points A and B. If the line perpendicular to AB and passing through the mid…

Let a circle C pass through the points (4, 2) and (0, 2), and its centre lie on 3x + 2y + 2 = 0. Then the length of the chord of the circle…

The absolute difference between the squares of the radii of the two circles passing through the point (-9, 4) and touching the lines x + y…

If the four distinct points (4, 6), (-1, 5), (0, 0) and (k, 3k) lie on a circle of radius r, then 10k + r^2 is equal to

Let C1 be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let C2 be the circle with center (1, 3) that…

Four points (2k,3k), (1,0), (0,0), nd (0,1) lie on a circle for k:

Consider a circle (x -)^2 + (y -)^2 = 50, where, 0. If the circle touches the line y + x = 0 at point P, whose distance from the origin is…

Equation of two diameters of a circle are 2x - 3y = 5 and 3x - 4y = 7. The line joining the points (- 227, -4) and ( 17, 3) intersects the…

The area (in sq. units) of the part of the circle x^2 + y^2 = 169 which is below the line 5x - y = 13 is ( /2) 65^2 + ( /) ^-1(12/13). The…

If the circles (x + 1)^2 + (y +2)^2 = r^2 and x^2 + y^2 - 4x - 4y + 4 = 0 intersect at exactly two distinct points, then:

Consider two circles C1: x^2 + y^2 = 25 and C2: (x-)^2 + y^2 = 16, where (5, 9). Let the angle between the two radii (one to each circle)…

If one of the diameters of the circle x^2 + y^2 - 10x + 4y + 13 = 0 is a chord of another circle C, whose center is the point of…

Let the circles C1: (x - a)^2 + (y - 3)^2 = r^2 and C2: (x - 8)^2 + (y - 1)^2 = (r/2)^2 touch each other externally at the point (6,6). If…

SECTION – A PHYSICS If the image of the point (-4, 5) in the line x + 2y = 2 lies on the circle (x + 4)^2 + (y - 3)^2 = r^2, then r is…

The locus of the midpoints of the chords of the circle C1: (x - 4)^2 + (y - 5)^2 = 4, which subtend an angle 1 at the centre of the circle…

The points of intersection of the line ax + by = 0, (a b) and the circle x^2 + y^2 - 2x = 0 are A(, 0) and B(1,). The image of the circle…

Points P(-3, 2), Q(9, 10), and R(, 4) lie on a circle C with PR as its diameter. The tangents to C at Q and R intersect at point S. If S…

Let the tangents at the points A((4, -11)) and B((8, -5)) on the circle x^2 + y^2 - 3x + 10y - 15 = 0 intersect at the point C. Then the…

A circle with center (2, 3) and radius 4 intersects the line x + y = 3 at points P and Q. If the tangents at P and Q intersect at S(,),…

Let y = x + 2, 4y = 3x + 6, and 3y = 4x + 1 be three tangent lines to the circle (x - h)^2 + (y - k)^2 = r^2. Then h + k is equal to:

Let a circle C1 be obtained on rolling the circle x^2 + y^2 - 4x - 6y + 11 = 0 upwards 4 units on the tangent T to it at the point (3, 2).…

If the center and radius of the circle | z - 2z - 3 | = 2 are respectively (,) and, then 3( + +) is equal to:

A circle passing through the point P(,) in the first quadrant touches the two coordinate axes at the points A and B. The point P is above…

If the tangents at the points P and Q on the circle x^2 + y^2 - 2x + y = 5 meet at the point R ( 94, 2), then the area of triangle PQR is:

Consider a circle C1: x^2 + y^2 - 4x - 2y = - 5. Let its mirror image in the line y = 2x + 1 be another circle C2: 5x^2 + 5y^2 - 10x - 10y…

An arc PQ of a circle subtends a right angle at its centre O. The midpoint of the arc PQ is R. If OP= u, OR= v and OQ= u+ v, then, ^2 are…

A line segment AB of length moves such that the points A and B remain on the periphery of a circle of radius. Then the locus of the point,…

Let A be the point (1, 2) and B be any point on the curve x^2 + y^2 = 16. If the centre of the locus of the point P, which divides the line…

Two circles in the first quadrant of radii r1 and r2 touch the coordinate axes. Each of them cuts off an intercept of 2 units with the line…

Let the centre of a circle C be (,) and its radius r < 8. Let 3x + 4y - 24 and 3x - 4y - 32 be two tangents and 4x + 3y = 1 be a normal to…

The number of common tangents to the circles x^2+y^2-18x-15y+131=0 and x^2+y^2-6x-6y-7=0 is