Question

Find the equation of the parabola by short cut method A) Focus (5,1) and Vertex (2,1)B) Focus (0,2) and Directrix: y=6

Answer 1

(A) Given Focus (5,1) and Vertex (2,1)

We are required to find the equation of the parabola

Substituting the values of h, k and f, we have

`\begin{gathered} x=(1)/(4(5-2))(y-1)^2+2 \\ \\ x=(1)/(4(3))(y-1)^2+2 \\ \\ x=(1)/(12)(y-1)^2+2 \\ \\ x=((y-1)^2)/(12)+2-------Vertex\text{ form} \end{gathered}`

Or in standard form, we have

`x=(y^2)/(12)-(y)/(6)+(25)/(12)`