If the chord y = mx + 1 of the circle x^{2}+y^{2}=1 subtends an angle of measure 45° at the major segment of the circle then value of m is [2002]
The centres of a set of circles, each of radius 3, lie on the circle x^{2}+y^{2}=25. The locus of any point in the set is
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The centre of the circle passing through (0, 0) and (1, 0) and touching the circle x^{2}+y^{2}=9 is [2002]
The equation of a circle with origin as a centre and passing through equilateral triangle whose median is of length 3a is
If the two circles ( x  1)^{2} + ( y  3)^{2} = r^{2 }and x^{2} + y^{2}  8 x + 2 y + 8 = 0 intersect in two distinct point, then[2003]
The lines 2 x  3y=5 and 3x  4 y = 7 are diameters of a circle having area as 154 sq.units.Then the equation of the circle is[2003]
If a circle passes through the point (a, b) and cuts the circle x^{2} + y^{2} = 4 orthogonally, then the locus of its centre is
A variable circle passes through the fixed point A( p,q) and touches xaxis . The locus of the other end of the diameter through A is [2004]
If the lines 2x + 3 y + 1 = 0 and 3x y  4=0 lie alon g diameter of a circle of circumference 10p, then the equation of the circle is [2004]
Intercept on the line y = x by the circle x^{2} + y^{2}  2x = 0 is AB. Equation of the circle on AB as a diameter is [2004]
If th e circles x^{2} + y^{2 }+ 2ax + cy + a = 0 and x^{2} + y^{2} – 3ax + dy – 1 = 0 intersect in two distinct points P and Q then the line 5x + by – a = 0 passes through P and Q for[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[2005]
If a circle passes through the point (a, b) and cuts the circle x^{2} + y^{2 }=^{ }p^{2 }orthogonally, then the equation of the locus of its centre is [2005]
If the pair of lines ax^{2} + 2 (a + b)xy + by 2 = 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 [2005]
If the lines 3x  4y  7=0 and 2x  3y  5=0 are two diameters of a circle of area 49π square units, the equation of the circle is [2006]
Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid points of the chords of the circle C that subtend an angle of at its center is
Consider a family of circles which are passing through the point (– 1, 1) and are tangent to xaxis. If (h, k) are the coordinate of the centre of the circles, then the set of values of k is given by the interval [2007]
The point diametrically opposite to the point P(1, 0) on the circle x^{2} + y^{2} + 2x + 4y – 3 = 0 is [2008]
The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is
If P an d Q are the points of intersection of the circles x^{2} + y^{2 }+ 3x + 7y+ 2p 5 =0 and x^{2 }+ y^{2} + 2x + 2y – p^{2 }= 0 then there is a circle passing through P, Q and (1, 1) for: [2009]
The circle x^{2} + y^{2} = 4x + 8y + 5 intersects the line 3x – 4y = m at two distinct points if [2010]
The two circles x^{2 }+ y^{2} = ax and x^{2 }+ y^{2} = c^{2} (c > 0) touch each other if [2011]
The length of the diameter of the circle which touches the xaxis at the point (1,0) and passes through the point (2,3) is: [2012]
The circle passing through (1, –2) and touching the axis of x at (3, 0) also passes through the point [JEE M 2013]
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 [JEE M 2014]
Locus of the image of the point (2, 3) in the line (2x – 3y + 4) + k (x – 2y + 3) = 0, k ∈ R, is a : [JEE M 2015]
The number of common tangents to the circles x^{2} + y^{2} – 4x – 6x – 12 = 0 and x^{2 }+ y^{2} + 6x + 18y + 26 = 0, is :[JEE M 2015]
The centres of those circles which touch the circle, x^{2} + y^{2} – 8x – 8y – 4 = 0, externally and also touch the xaxis,lie on: [JEE M 2016]
If one of the diameters of the circle, given by the equation, x^{2} + y^{2 }– 4x + 6y – 12 = 0, is a chord of a circle S, whose centre is at (–3, 2), then the radius of S is: [JEE M 2016]
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447 docs930 tests
