Let $x^2+y^2+Ax+By+C=0$ be a circle passing through $(0,6)$ and touching the parabola $y=x^2$ at $(2,4)$. Then $A+C$ is equal to
Step-by-Step Solution
Key Concept: Circle passes through (0,6); tangent to parabola at (2,4) means same tangent line
Tangent to $y=x^2$ at $(2,4)$: $y=4x-4$. Circle through $(0,6)$ and $(2,4)$ touching parabola gives $A+C=16$.
Correct Answer: 1