The circle passing through the point (-1,0) and touching the Y -axis at (0,2) , also passes through the point

Step-by-step solution

Equation of circle passing through a point (x₁, y₁ ) and touching the straight line L , is given by (x-x₁ )^2+ (y-y₁ )^2= L=0 Equation of circle passing through (0,2) and touching x=0 . Now, (x-0)^2+(y-2)^2+ x=0 (i) Also, it passes through (-1,0) . So, 1+4- =0 =5 Eq. (i) becomes, aligned & x^2+y^2-4 y+4+5 x=0 x^2+y^2+5 x-4 y+4 & =0 aligned For x -intercept, put y=0 , array rlrl & x^2+5 x+4 & =0 & & (x+1)(x+4) & =0 & & x & =-1,-4 array