Q60 / 150 · MHT CET 2008 · Mathematics

The focal distance of a point on the parabola $y^{2}=16 x$ whose ordinate is twice the abscissa, is

  • A
    6
  • Correct answer
    B
    8
  • C
    10
  • D
    12

Solution

Given curve is $y^{2}=16 x$. Let the point be $(h, k)$. But $2 h=k$, then $k^{2}=16 h$ $$ \begin{aligned} \Rightarrow & & 4 h^{2} &=16 h \\ \Rightarrow & & h &=0, h=4 \\ \Rightarrow & & k &=0, k=8 \end{aligned} $$ $\therefore$ Points are $(0,0),(4,8)$. Hence, focal distance are respectively $$ 0+4=4,4+4=8 $$ $(\because$ focal distance $=h-a)$

Hence, the correct answer is option: 'B'.

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