Question

The circles x² + y² + x + y =0 and x² + y² + x - y = 0 intersect at an angle of -

a) π/6

b) π/4

c) π/3

d) π/2

Answer 1

Applying the formula for Angle of intersection of two circles:

The angle of intersection between two circles S = 0 ans S’ = 0 is defined as the angle between their tangents at their point of intersection.

If S =  x² + y² + 2g₁x + 2f₁y + c₁ = 0 

and S“ ≡ x² + y² + 2g₂x + 2f₂y + c₂ = 0, are two cricles with radii r₁, r₂ and ‘d’ is the distance between their centres then the angle of intersection θ between them is given by

cos θ = (r₁² + r₂² – d²)/ 2r₁r₂  or   cos θ = 2(g₁g₂ + f₁f₂) – (c₁ + c₂)/ 2√(g₁² + f₁² – c₁) √(g₂² + f₂² – c₂) 

From given equation we have

q1=1/2, f1=1/2, c1=0

q2=1/2, f2=1/2, c2=0

putting the value in angle equation we get

cos θ = 0

So, θ = 90^o

Hence, option (d) is correct.