Question

what eqwation of a parabola with a focus(6,-2) and a directrix x=-2

Answer 1

Answer:

The equation of the parabola

( y +2 )² = 16 (x-2)

Step-by-step explanation:

Step(i):-

Given the focus of the Parabola ( 6, -2 )

we know that the Focus of the Parabola

                ( h + a , k ) = ( 6 , -2 )

Comparing

              h + a = 6 ...(i)

          and  k = -2

Given directrix of the parabola

           x = -2

The  directrix of the parabola  x = h - a = -2

        h - a = -2 ...(ii)

Adding (i) and (ii) equations , we get

    h + a + h-a = 6 -2

                2 h = 4

           ⇒    h  = 2

Substitute 'h' = 2 in equation (i) , we get

          h + a = 6

          2 + a = 6

                a = 6 -2 =4

Step(ii):-

The equation of the parabola having Vertex ( h,k) = (2 , -2) and a = 4

$(y-k)^{2} = 4a ( x-h)$

( y - (-2))² = 4 (4) ( x -2)

Final answer:-

The equation of the parabola

$(y-(-2))^{2} = 4(4) ( x-2)$

( y +2 )² = 16 (x-2)