Angle between Two Circles

IMPORTANT

Angle between Two Circles: Overview

This topic covers concepts such as Angle of Intersection of Two Circles, Common Chord of Two Circles, Equation of Common Chord of Two Circles, Length of Common Chord of Two Circles and Condition of Orthogonality of Two Circles.

Important Questions on Angle between Two Circles

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IMPORTANT

The equation of the common chord of the pair of circles: (x-a)2+(y-b)2=c2, and (x-b)2+(y-a)2=c2(ab) is

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The equation of the circle which cuts orthogonally the circle x2+y2-4x+2y-7=0 and having the centre at (2,3) is

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The equation of the circle which passes through the points (2,0),(0,2) and orthogonal to the circle 2x2+2y2+5x-6y+4=0 is

MEDIUM
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The equation of the circle passing through the origin, having its centre on the line x+y=4 and intersecting the circle x2+y2-4x+2y+4=0 orthogonally is

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The equation of the circle which passes through the origin and intersects the circles, x2+y2-4x-6y-3=0, and x2+y2-8y+12=0 orthogonally is

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The equation of the circle which passes through the origin and intersects the circles, orthogonally: x2+y2-4x+6y+10=0, and x2+y2+12y+6=0 is

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The angle between the circles given by the equations: x2+y2+6x-10y-135=0, and x2+y2-4x+14y-116=0 is

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If the angle between the circles given by the equations: x2+y2-12x-6y+41=0,x2+y2+4x+6y-59=0 is πk, then write the value of k.

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Find 'k' if the following pairs of circles are orthogonal: x2+y2+4x+8=0,x2+y2-16y+k=0.

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Find 'k' if the following pairs of circles are orthogonal: x2+y2-5x-14y-34=0,x2+y2+2x+4y+k=0.

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Find 'k' if the following pairs of circles are orthogonal: x2+y2-6x-8y+12=0,  x2+y2-4x+6y+k=0.

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Find 'k' if the following pairs of circles are orthogonal: x2+y2+2by-k=0,x2+y2+2ax+8=0.

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In List-I, a pair of circles is given in A, B, C and in List-II, angle between those pair of circles is given. Match the items from List-I to List-II

List-I List-II
(A) x-22+y2=2
x-22+y-12=1
I 90°
(B) x2+y2-6x-6y+9=0
x2+y2-4x+4y-9=0
II 135°
(C) x2+y2+4x-14y+28=0
x2+y2+4x-5=0
III 60°
    IV 30°

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The possible number of values of a for which the common chord of the circles x2+y2=8 and x-a2+y2=8 subtends a right angle at the origin is

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Let PQ be the common chord of the circles S1:x2+y2+2x+3y+1=0 and S2:x2+y2+4x+3y+2=0, then the perimeter (in units) of the triangle C1PQ is equal to where,C1=-1,-32

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The locus of the centre of the circle which cuts the parabola y2=4x orthogonally at (1, 2) will pass through the point

EASY
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If the circles x2+y2-2λx-2y-7=0 and 3x2+y2-8x+29y=0 are orthogonal then λ=

EASY
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If the angle between the circles x2+y2-2x-4y+c=0 and x2+y2-4x-2y+4=0 is 60°, then c is equal to

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The length of the common chord of the two circles x-a2+y2=a2  and  x2+y-b2=b2 is

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IMPORTANT

The length of the common chord of the two circles x-a2+y2=a2  and  x2+y-b2=b2 is