Question

Find the vertex and focus of the
parabola:
x² + 14x-8y + 65 = 0

I can’t figure this out!!!

Answer 1

Answer:

$\boxed {Vertex = (-7, 2)}\\\boxed {Focus = (0, \frac{49}{8})}$

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)