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for the equation: (y - 2)2 = 8(x - 5); identify focusQuestion 9Select one:(0 , 0)(2 , 5)(2 , 8)(7 , 2)Clear my choice◄ weekend sheet t3 w8Jump to...

Question

For the equation:

(y−2)2=8(x−5);(y - 2)^2 = 8(x - 5); Identify focus

Question 9 Select one:

  • (0 , 0)
  • (2 , 5)
  • (2 , 8)
  • (7 , 2)

Clear my choice

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Solution

The given equation is in the form of a parabola equation (y - k)² = 4a(x - h), where (h, k) is the vertex of the parabola and 'a' is the distance from the vertex to the focus.

In the given equation, (y - 2)² = 8(x - 5), we can see that h = 5, k = 2 and 4a = 8.

So, a = 8/4 = 2.

The focus of a parabola that opens rightward (as this one does, because the y-term is squared) is given by the point (h + a, k).

Substituting the values we have, the focus is at (5 + 2, 2) = (7, 2).

So, the focus of the given parabola is (7, 2).

This problem has been solved

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