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Question: Answered & Verified by Expert
The point of contact of the tangent $18 x-6 y+1=0$ to the parabola $y^2=2 x$ is
MathematicsParabolaJEE Main
Options:
  • A $\left(\frac{-1}{18}, \frac{-1}{3}\right)$
  • B $\left(\frac{-1}{18}, \frac{1}{3}\right)$
  • C $\left(\frac{1}{18}, \frac{-1}{3}\right)$
  • D $\left(\frac{1}{18}, \frac{1}{3}\right)$
Solution:
2502 Upvotes Verified Answer
The correct answer is: $\left(\frac{1}{18}, \frac{1}{3}\right)$
Let point of contact be $(h, k)$, then tangent at this point is $k y=x+h$.
$x-k y+h=0 \equiv 18 x-6 y+1=0$
or $\frac{1}{18}=\frac{k}{6}=\frac{h}{1} \quad$ or $\quad k=\frac{1}{3}, \quad h=\frac{1}{18}$

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