MCQ (Previous Year Questions) - Circle (Competition Level 1) - JEE MCQ

If a circle passes through the point (a, b) and cuts the circle x² + y² = 4 orthogonally, then the locus of its centre is

-[AIEEE-2004]

A variable circle passes through the fixed point A(p, q) and touches x-axis. The locus of the other end of the diameter through A is -

[AIEEE-2004]

If the lines 2x + 3y + 1 = 0 and 3x – y – 4 = 0 lie along diameters of a circle of circumference 10π, then the equation of the circle is -

[AIEEE-2004]

If the circles x² + y² + 2ax + cy + a = 0 and x² + y² – 3ax + dy – 1 = 0 intersect in two distinct point P and Q then the lines 5x + by – a = 0 passes through P and Q for -

[AIEEE-2005]

A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is -

[AIEEE-2005]

If a circle passes through the point (a, b) and cuts the circle x² + y² = p² orthogonally, then the equation of the locus of its centre is -

[AIEEE-2005]

If the pair of line ax² + 2(a + b)xy + by² = 0 lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then

[AIEEE-2005]

If thel ines 3x – 4y – 7 = 0 and 2x – 3y – 5 = 0 are two diameters of a circle of area 49 π square units, the equation of the circle is -

[AIEEE-2006]

The triangle PQR is inscribed in the circle, x²+y² = 25. If Q and R have co-ordinates (3, 4) & (–4, 3) respectively, then √QPR is equal to

[JEE 2000(Scr.), 1 + 1]

If the circles, x² + y² + 2x + 2ky + 6 = 0 & x² + y² + 2ky + k = 0 intersect orthogonally, then ‘k’ is

Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle then 2r equals.

[JEE 2001 (Scr.), 1]

Let 2x² + y² – 3xy = 0 be the equation of a pair of tangents drawn from the origin 'O' to a circle of radius 3 with centre in the first quadrant. If A is one of the points of contact, find the length of OA.

If the tangent at the point P on the circle x² + y² + 6x +6y = 2 meets the straight line 5x – 2y + 6 = 0 at a point Q on the y-axis, then the length of PQ is

If a > 2b > 0 then the positive value of m for which   i s a common tangent to  x² + y² = b² and (x - a)² + y² = b² is

[JEE 2002 (Scr.)]

The radius of the circle, having centre at (2, 1), whose one of the chord is a diameter of the circle x₂ + y₂ – 2x – 6y + 6  = 0

[JEE 2004(Scr.)]

Tangents drawn from the point P(1, 8) to the circle x² + y² – 6x – 4y – 11 = 0 touch the circle at the points A and B. The equation of the circumcircle of the triangle PAB is

The centres of two circles C₁ and C₂ each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of C₁ and C₂ and C be a circle touching circles C₁ and C₂ externally. If a common tangent to C₁ and C passing through P is also a common tangent to C₂ and C, then the radius of the circle C is

[JEE 2009]

Two parallel chords of a circle of radius 2 are at a distance 3 + 1 apart. If the chords subtend at the center, angles of π/k andk 2π/k , where k > 0, then the value of [k] is
{Note : [k] denotes the largest integer less than or equal to k}

[JEE 2010]

The circle passing through the point (–1, 0) and touching the y-axis at (0, 2) also passes through the point

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x – 5y = 20 to the circle x² + y² = 9 is

[JEE 2012]

A tangent PT is drawn to the circle x² + y² = 4 at the point P (√3, 1) . A straight line L, perpendicular toPT is a tangent to the circle (x – 3)² + y² = 1. A possible equation of L is

[JEE 2012]