Question

For how many values, of p, the circle `x^2+y^2+2x+4y-p=0` and the coordinate axes have exactly three common points?

Answer 1

for circle 1
`0^2+0^2+0+0-p=0`
`p=0`
for circle 2
`g^2-c=0`and`f^2-c>0`
`1^2-(-p)=0`
`p=-1`
`4-(-p)>0`
`p>-4`
for circle 3
`f^2-0=0`
`4-(-p)=0`
`p=-4`
`g^2-c>0`
`1^2-(-p)>0`
`p>-1`.