Question

\[
  {\text{. If a parabola touch three given straight lines, prove that each of the lines joining the points }} \\
  {\text{of contact passes through a fixed point}}{\text{.}} \\
\]

Answer 1

\[
  {\text{If two of the tangents are the axis then equation of parabola is}} \\
  \sqrt {\dfrac{x}{a}} + \sqrt {\dfrac{y}{b} = 1} \\
  {\text{If the third tangent is }}\dfrac{x}{f} + \dfrac{y}{g} = 1 \\
  {\text{Then, the condition for the tangency is}} \\
  \dfrac{f}{a} + \dfrac{g}{b} = 1 \\
  {\text{So, the line }}\dfrac{x}{a} + \dfrac{y}{b} = 1{\text{ always passes through }}(f,g) \\
  {\text{Note: In this type of question always start with two static straight lines}} \\
  {\text{ then introduce third line with condition}}{\text{.}} \\
\]