Question

The centre of the circle passing through the point (0, 1) and touching the curve $y=x^2$ at (2, 4) is

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is C

Tangent to the parabola $y=x^2$ at (2,4) is
$\frac{1}{2}$(y+4)=x.2 or 4x-y-4=0
It is also a tangent to the circle so that the centre lies on the normal through (2,4) whose equation is
x+4y =$\lambda$, where 2+16 = $\lambda$
$\therefore$ x+4y=18 is the normal on which lies (h,k).
$\therefore$ h+4k=18$...\left(i\right)$