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3 years ago

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:

The equation of the Parabola

(y - 6 )² = 8 (x -6)

Step-by-step explanation:

Step(i):-

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

Step(ii):-

The equation of the Parabola ( h,k) = (6 , 6)

( y - k )² = 4 a ( x - h )

(y - 6 )² = 4 (2) (x -6)

(y - 6 )² = 8 (x -6)

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