<s>[INST] Find the radius Consider the parabola $y=x^2$ and a circle which is tangent to the parabola at the points $(1,1)$ and $(-1,1)$.Find the radius of circle.
My try:I write the general equation of circle 
$(x-h)^2+(y-k)^2=r^2$
and substitute the points $(1,1)$ and $(-1,1)$ in the equation of circle,i find $h=0$.
Now further what i should do to find r?
 [/INST] Substitute $(1,1),(-1,1)$ in $(x-h)^2+(y-k)^2=r^2$
you will get 
$h^2+k^2-2h-2k+2=r^2$  and  $h^2+k^2+2h-2k+2=r^2$
From here you get $h=0$, substitute this in one of the above to obtain 
$k^2-2k+2=r^2$ 
$m_1$=slope of tangent line at $(1,1)=2$  (here use the $y=x^2$)
Where $m_2$=the slope of radial line at  $(1,1)= 1-k$ (here use the equation of circle) 
since $m_1m_2=-1$,  so we have $k=\frac{3}{2}$
Substitute  $k=\frac{3}{2}$ in 
$$k^2-2k+2=r^2$$
Finally you will get the answer $r=\frac{\sqrt{5}}{2}$
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