The equation of the parabola is (x - 6)² = 6(y + 5.5).
Given that, a focus at (6,-4) and a directrix at y= -7.
We need to find the equation for a parabola.
<h3>What are focus and directrix?</h3>
Parabolas are commonly known as the graphs of quadratic functions. They can also be viewed as the set of all points whose distance from a certain point (the focus) is equal to their distance from a certain line (the directrix).
The standard form of the equation of the parabola is (x - h)² = 4p(y - k), where
The vertex of the parabola is (h , k)
The focus is (h, k + p)
The directrix is at y = k - p
∵ The focus of the parabola is at (6, -4)
The coordinates of the focus are (h, k + p)
∴ h = 6
∴ k + p = -4 ⇒ (1)
∵ The directrix of the parabola is at y = -7
The directrix is at y = k - p
∴ k - p = -7 ⇒ (2)
Solve the system of equations to find k and p
Add equations (1) and (2) to eliminate p
∴ 2k = -11
Divide both sides
∴ k = -5.5
Substitute the value of k in equation (1) to find p
∵ -5.5 + p = -4
Add 5.5. to both sides
∴ p = 1.5
∵ The form of the equation is (x - h)² = 4p(y - k)
Substitute the values of h, k, and p in the form
∴ (x - 6)² = 4(1.5)(y - -5.5)
∴ (x - 6)² = 6(y + 5.5)
Therefore, the equation of the parabola is (x - 6)² = 6(y + 5.5).
To learn more about an equation of parabola visit:
brainly.com/question/4074088.
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Your question is incomplete, probably the complete question/missing part is:
Write the equation for a parabola with a focus at (6,-4) and a directrix at y= -7
