Question

If the parabola $y=x^2$ is tangent to the circle $x^2+(y-1{)}^2=c$, then the value of $c$ is equal to

• A. $\frac{4}{5}$
• B. $\frac{3}{4}$
• C. $\frac{2}{3}$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

Substitute $x^2=y$ to get $y+(y-1{)}^2=c$
or $y^2-y+1-c=0$.
$D=1-4(1-c)=0$
$-3+4c=0$
$c=\frac{3}{4}$