Question

Which equation represents a parabola with its vertex at (1, –5) and its focus at (1, 0)?

a. 1/20(y+5) = (x-1)^2
b. 20(y+5) = (x-1)^2
c. -20(y+5) = (x-1)^2
d. -1/20(y+5) = (x-1)^2

Answer 1

Answer: b. 20(y+5) = (x-1)^2

Step-by-step explanation: just took review

Answer 2

The equation that represents the parabola is 20(y + 5) = (x - 1)² ⇒ b

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