Question

find the angle between circles x^2+y^2=a^2 and x^2+y^2=ax+ay

Answer 1

hey there...
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here is ur answer
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Answer 2

Answer:

135°

Step-by-step explanation:

Concept= Angle between Circle

Given= Equations of two Circle

To Find= Angle between two circle

Explanation=

We have been given the equation of two circles as x^2+y^2=a^2 and x^2+y^2=ax+ay.

We take two circle as S1 and S2

S1= x^2+y^2=a^2

=> x^2+y^2-a^2 =0

Centre of S1 is c1=(0,0)

Radius of S1 is r1 = a

S2= x^2+y^2-ax-ay=0

Centre of S2 is c2= (a/2 , a/2)

Radius of S2 is r2= (a/√2)

Difference in center is d which is √(a/2)²+(a/2)² = a/√2

Therefore the angle Ф will be cosФ= (d²-r1²-r2²)/2r1r2

=>((a/√2)² - a² - (a/√2)²)/2aa/√2 =  -1/√2

cosФ= cos135°

Ф=135°

Therefore the angle between two circle x^2+y^2=a^2 and x^2+y^2=ax+ay is 135°

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