Circle

A line drawn through the point P(4, 7) cuts the circle x2 + y2 = 9 at the points A and B. Then PA⋅PB is equal to :

The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60o. If the area of the quadrilateral is \(4\sqrt 3\), then the perimeter
of the quadrilateral is :

If a point P has co-ordinates (0, \(-\)2) and Q is any point on the circle, x2 + y2 \(-\) 5x \(-\) y + 5 = 0, then the maximum value of (PQ)2 is :

If two parallel chords of a circle, having diameter 4units, lie on the opposite sides of the center and subtend angles \({\cos ^{ - 1}}\left( {{1 \over 7}} \right)\) and sec\(-\)1 (7) at the center respectivey, then the distance between the...

The radius of a circle, having minimum area, which touches the curve y = 4 – x2 and the lines, y = |x| is :

A circle passes through (−2, 4) and touches the y-axis at (0, 2). Which one of the following equations can represent a diameter of this circle?

Equation of the tangent to the circle, at the point (1, −1), whose centre is the point of intersection of the straight lines x − y = 1 and 2x + y = 3 is :

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 :

The centres of those circles which touch the circle, \({x^2} + {y^2} - 8x - 8y - 4 = 0\), externally and also touch the \(x\)-axis, lie on :

Locus of the image of the point \((2, 3)\) in the line \(\left( {2x - 3y + 4} \right) + k\left( {x - 2y + 3} \right) = 0,\,k \in R,\) is a :

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 :

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 circle passing through \((1, -2)\) and touching the axis of \(x\) at \((3, 0)\) also passes through the point :

The length of the diameter of the circle which touches the \(x\)-axis at the point \((1, 0)\) and passes through the point \((2, 3)\) is :

The two circles x2 + y2 = ax, and x2 + y2 = c2 (c > 0) touch each other if :

The circle \({x^2} + {y^2} = 4x + 8y + 5\) intersects the line \(3x - 4y = m\) at two distinct points if :

Three distinct points A, B and C are given in the 2 -dimensional coordinates plane such that the ratio of the distance of any one of them from the point \((1, 0)\) to the distance from the point \((-1, 0)\) is equal to \({1 \over 3}\). Then...

If \(P\) and \(Q\) 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 :

The point diametrically opposite to the point \(P(1, 0)\) on the circle \({x^2} + {y^2} + 2x + 4y - 3 = 0\) is :

The differential equation of the family of circles with fixed radius \(5\) units and centre on the line \(y = 2\) is :

Consider a family of circles which are passing through the point \((-1, 1)\) and are tangent to \(x\)-axis. If \((h, k)\) are the coordinate of the centre of the circles, then the set of values of \(k\) is given by the interval :

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 \({{2\pi } \over 3}\) at its center is :

If the lines \(3x - 4y - 7 = 0\) and \(2x - 3y - 5 = 0\) are two diameters of a circle of area \(49\pi\) square units, the equation of the circle is :

If the circles \({x^2}\, + \,{y^2} + \,2ax\, + \,cy\, + a\,\, = 0\) and \({x^2}\, + \,{y^2} - \,3ax\, + \,dy\, - 1\,\, = 0\) intersect in two ditinct points P and Q then the line 5x + by - a = 0 passes through P and Q for :

If the pair of lines \(a{x^2} + 2\left( {a + b} \right)xy + b{y^2} = 0\) 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 :

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 :

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 :

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 :

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 :

If the lines 2x + 3y + 1 + 0 and 3x - y - 4 = 0 lie along diameter of a circle of circumference \(10\,\pi\), then the equation of the circle is :

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 :

The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then the equation of the circle is :

If the two circles \({(x - 1)^2}\, + \,{(y - 3)^2} = \,{r^2}\) and \(\,{x^2}\, + \,{y^2} - \,8x\, + \,2y\, + \,\,8\,\, = 0\) intersect in two distinct point, then :

The equation of a circle with origin as a center and passing through an equilateral triangle whose median is of length \(3\)\(a\) is :

The centre of the circle passing through (0, 0) and (1, 0) and touching the circle \({x^2}\, + \,{y^2} = 9\) is :

If the chord y = mx + 1 of the circle \({x^2}\, + \,{y^2} = 1\) subtends an angle of measure \({45^ \circ }\) at the major segment of the circle then value of m is :

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 :