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balandron [24]
3 years ago
11

A parabola can be drawn given a focus of (8, 6) and a directrix of x=4. Write the equation of the parabola

Mathematics
1 answer:
Orlov [11]3 years ago
3 0

Answer:

<em>The equation of the Parabola</em>

 <em>(y - 6 )² = 8 (x -6)</em>

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given directrix  x = 4

we know that    x = h - a = 4

               h -a =  4  ...(i)

Given Focus  = ( 8,6)

we know that the Focus of the Parabola

         ( h + a , k ) = ( 8,6)

   comparing  h + a = 8 ...(ii)

                  k = 6

solving (i) and (ii) and adding

   h - a + h+ a = 8 +4

           2 h = 12

              h =6

   Put h = 6 in equation (i)

  ⇒     h - a =4

  ⇒   6 - 4 = a

  ⇒      a = 2

<u><em>Step(ii):-</em></u>

<em>The equation of the Parabola ( h,k) = (6 , 6)</em>

<em>( y - k )² = 4 a ( x - h )</em>

<em>(y - 6 )² = 4 (2) (x -6)</em>

<em>(y - 6 )² = 8 (x -6)</em>

<u><em></em></u>

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