AP EAMCET Coordinate Geometry: System of Circles — practice questions
69 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAMCET Coordinate Geometry: System of Circles in the app →Find the radical axis of x²+y²=9 and x²+y²-4x-5=0.Two circles of radius 2 are centred at (0,0) and (3,0). Their radical axis isThe radical axis of two circles is related to their line of centres asCircles x²+y²=25 and (x-6)²+y²=25 meet at two points. Their common chord has lengthTwo circles of radius 5 have centres 8 units apart. Their common chord has lengthThe length of the tangent from (5,5) to x²+y²-2x-4y-4=0 isFind the tangent length from the origin to x²+y²-6x-8y+9=0.The power of the point (7,1) with respect to x²+y²=25 isThe radical centre of x²+y²=1, x²+y²-4x+3=0 and x²+y²-4y+3=0 isx²+y²+2x+4y+1=0 cuts x²+y²-6x-4y+k=0 orthogonally. Then k equalsTwo circles of radii 3 and 4 cut orthogonally. Their centres are how far apart?Orthogonal circles have centres 10 apart and one has radius 6. The other radius isTwo circles are orthogonal when their tangents at a common point areCircles through the common points of circle S=0 and line L=0 form the familyCircle through the origin and the common points of x²+y²=4 and x+y=1 isThe limiting points of the coaxal system x²+y²+2λx+9=0 areAll circles in one coaxal system share the sameLimiting points of a coaxal system are point circles of radiusThe radical axis of two touching circles isThe radical axis of two circles that intersect at two points isCentres of all circles cutting two given circles orthogonally lie on theirFor two circles of equal radius, the radical axis is the ___ of the segment joining the centres.Jakob Steiner introduced the power of a point in the yearA point lying on a circle has how many tangents through it?Tangents from P touch a circle (centre O) at T and S, with ∠TPS = 50°. Find ∠TOS.From P a secant meets a circle at A and B with PA = 4 and PB = 9. The tangent length from P isFrom P a tangent of length 10 is drawn, and a secant meets the circle at A (near) and B with PA = 5. Chord AB Chords AB and CD meet at P inside a circle with AP = 6, PB = 4, CP = 3. Then PD equalsThe line 3x+4y=k touches x²+y²=25 only when k equalsThe chord of contact from (5,0) to x²+y²=9 isTwo circles of radii 3 and 2 have centres 5 apart. Common tangents:A circle of radius 2 lies inside one of radius 6, centres 1 apart. Common tangents:Radii 9 and 6, centres 17 apart. Length of a transverse common tangent?Radii 7 and 1 with centres 10 apart: the direct common tangent measuresThe circles x²+y²=4 and (x-5)²+y²=9The locus of points with equal tangent lengths to x²+y²=4 and x²+y²-4x=0 isFrom a point of the radical axis outside two circles, the two tangent lengths areIf the centres of three circles are collinear, their three radical axes areA circle centred at the radical centre with radius equal to the common tangent length is, to the three circlesThe power of the centre of a circle of radius 7 with respect to itself isThe power of a point lying exactly on a circle isA point 13 units from the centre of a circle of radius 5 has powerRadical axis of x²+y²+6x-4y-3=0 and x²+y²-2x+8y+5=0 isA tangent is drawn from (10,0) to x²+y²=64. Its length isTangent length from (6, 8) to x² + y² = 36 is?Radical axis of x² + y² + 2x + 3y - 5 = 0 and x² + y² + 4x + y - 7 = 0?Equal-radius circles have a radical axis that is the?Two circles touching at a point have radical axis equal to the?x² + y² = 1 and x² + y² - 6x + 5 = 0 meet how?What did J. Steiner call the radical axis?Radical axes of three circles with non-collinear centres?Circles with centres on a line and one radical axis form?A pencil of circles shares which common feature?Which pencil has all circles through the same two points?Generators that never intersect define which pencil?Circles all tangent at one common point form which pencil?The point circles of a hyperbolic pencil are called?A circle orthogonal to two circles of a pencil is?The orthogonal pencil of an elliptic pencil is?Three circles with one shared axis lie in a pencil if?Monge's theorem: outer similarity points of three circles?In the chords and secants theorems, power of a point is the?The radical plane of two spheres has equal what?The common point of a pencil of lines is its?The line shared by every plane of a pencil of planes is its?Points in general position that fix a conic?Base points that define a pencil of conics?Four points fix a unique sphere if they are?The plane of the common circle of two spheres is the?