Find the locus of centres of circle touching the lines x + 2y = 0 and x-2y = 0
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Answer:
Step-by-step explanation:
First find the centre of circles:
Circle 1 : x^2+y^2+2x+4y+2=0
=>(x^2+2x+1)+(y^2+4y+4)-3=0
=>(x+1)^2+(y+2)^2=3
centre of circle is (-1,-2)
similarly for circle 2:
x^2+y^2+3x+3y+1=0
=>(x^2+2.3/2 .x+(3/2)^2)+(y^2+2.3/2*y+(3/2)^2)+1–9/2=0
=>(x+3/2)^2+(y+3/2)^2=7/2
hence centre of circle is ( -3/2,-3/2)
As per given information the centres (-1,-2) and (-3/2,-3/2) lies on the circles , that means there might be n number of circles passing through these points and forming a common chord for all the circles.
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