Question

If the circle $x^2+y^2+2x+4y-p=0$ and the coordinate axes have exactly three common points, then p =

• A. 1
• B. -1
• C. 2
• D. -4

Answer 1

The correct option is B -1

I. Circle P.T. origin $\Rightarrow$ P = 0
II. Touch y-axis and cuts x-axis
$\Rightarrow f^2-c=0$ and $g^2-c>0$
$\Rightarrow p=-4$ and $1+p>0$ (not possible)
III. Touch x-axis and cuts y-axis
$\Rightarrow f^2-c>0$ and $g^2-c=0$
$\Rightarrow p>-4$ and $p=-1$.