Question

Find the locus of centres of circle touching the lines x + 2y = 0 and x-2y = 0

Answer 1

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.