Question

The parabola $y^2-2x-6y+5=0$ has

• A. Focus $\equiv (-\frac{3}{2},3)$
• B. Vertex $\equiv (-2,3)$
• C. Directrix $x=-\frac{5}{2}$
• D. all of these

Answer 1

The correct option is D all of these

The given equation of the parabola can be written in the form

${(y-3)}^2=2(x+2)\Rightarrow {(y-3)}^2=4.\frac{1}{2}(c+2)$

So, $a=\frac{1}{2}$

Coordinates of vertex are $x+2=0,y-3=0\Rightarrow (-2,3)$

Coordinates of focus are $x+2=\frac{1}{2},y-3=0\Rightarrow (-\frac{3}{2},3)$

Equation of directrix is $x+2=-\frac{1}{2}\Rightarrow x=-\frac{5}{2}$