Question

The length of a focal chord of the parabola $y^2=4ax$ at a distance ‘b’ from the vertex is ‘c’, then

• A. $2a^2=bc$
  
• B. $a^3=b^{2}c$
  
• C. $b^2=ac$
  
• D. $b^{2}c=4a^3$

Answer 1

The correct option is D $b^{2}c=4a^3$

Let the angle made by focal chord with x – axis be ${}^{\prime }{\theta }^{\prime }$
$\therefore sin\theta =\frac{b}{a}$
Length of focal chord, $c=4acose{c}^2\theta$
$\Rightarrow c=4a{\left(\frac{a}{b}\right)}^2\Rightarrow b^{2}c=4a^3$