Question

The distance between the vertex and the focus of the parabola $x^{2}-2\, x+3\, y-2=0$ is

• A. $\frac{4}{5}$
• B. $\frac{3}{4}$
• C. $\frac{1}{2}$
• D. $\frac{5}{6}$

Answer 1

Answer: (B)

Equation of parabola is
$x^{2}-2\, x+ 3\, y-2 =0 $
$\Rightarrow x^{2}-2 x+1 =-3\, y+2+1 $
$\Rightarrow (x-1)^{2} =-3(y-1)$
Distance between the vertex and focus of parabola
$=\frac{1}{4} \times$ Length of latusrectum
$=\frac{1}{4} \times 3=\frac{3}{4}$