Answer:
[tex]\boxed {Vertex = (-7, 2)}\\\boxed {Focus = (0, \frac{49}{8})}[/tex]
Step-by-step explanation:
Completing the square :
x² + 14x - 8y + 65 = 0
x² + 14x + 49 - 49 - 8y + 65 = 0
(x + 7)² - 8y + 16
(x + 7)² = 8y - 16
⇒ x = -7, y = 2 (Vertex)
Finding a :
⇒ x² = 4ay
⇒ (-7)² = 4(2)a
⇒ a = 49/8
Finding the focus :
⇒ (0, a)
⇒ (0, 49/8) (Focus)
