Answer:
The equation that represents the parabola is 20(y + 5) = (x - 1)² ⇒ b
Step-by-step explanation:
The 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 at (h, k + p)
Let us use the form above to solve the question
∵ The vertex of the parabola is (1, -5)
→ That mean (h, k) is (1, -5)
∴ h = 1 and k = -5
∵ Its focus is at (1, 0)
→ That means (h, k + p) is (1, 0)
∴ k + p = 0
→ Substitute the value of k
∴ -5 + p = 0
→ Add 5 to both sides
∵ -5 + 5 + p = 0 + 5
∴ p = 5
→ Substitute the values of h, k, p in the form above
∵ (x - 1)² = 4(5)(y - -5)
→ Remember that (-)(-) = (+)
∴ (x - 1)² = 20(y + 5)
→ Switch the two sides
∴ 20(y + 5) = (x - 1)²
∴ The equation that represents the parabola is 20(y + 5) = (x - 1)²
