The equation of the parabola is (x - 6)² = 6(y + 5.5)
Step-by-step explanation:
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 bith 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)
The equation of the parabola is (x - 6)² = 6(y + 5.5)
Learn more:
You can learn more about the parabola in brainly.com/question/9390381
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