Question

The equation of the directrix of the parabola whose vertex and focus are (1, 4) and (2, 6) respectively is 

Options

• x + 2y = 4 

• x − y = 3 1

•  2x + y = 5 

• x + 3y = 8 

Answer 1

x + 2y = 4 

Given:
The vertex and the focus of a parabola are (1, 4) and (2, 6), respectively.
∴ Slope of the axis of the parabola = \[\frac{6 - 4}{2 - 1} = 2\] 

Slope of the directrix = \[\frac{- 1}{2}\] 

Let the directrix intersect the axis at K (r, s). 

\[\frac{r + 2}{2} = 1, \frac{s + 6}{2} = 4\]
\[ \Rightarrow r = 0, s = 2\]

Equation of the directrix: 

\[\left( y - 2 \right) = \frac{- 1}{2}\left( x - 0 \right)\] 

\[\Rightarrow\] x + 2y = 4