ParabolaHardBloom L3
Question
A circle $C$ passes though the points of intersection of the parabola $y + 1 = (x - 4)^{2}$ and the $x$-axis. The length of tangent from origin to $C$ is :
Options
A.8
B.15
C.$\sqrt{8}$
D.$\sqrt{15}$
Solution
Sol. [Key Concept: Tangent length from $O$ $= \sqrt{|constant\ term|}$ of the circle $= \sqrt{product\ of\ the\ x - intercepts}$ (power of the origin).]
$$\begin{matrix} (OT)^{2} & \ = (OA)(OB) \\ = 3 \times 5 & \ = 15 \\ \Rightarrow \ OT & \ = \sqrt{15} \end{matrix}$$
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