Please Check My Answers!!!

Question

What is the type of conic section is given by the equation x^2-9y^2=900 and what is
the domain and range?
Answer: Type is hyperbola, Domain is all real values of x, not sure what the range is. Please explain how to find these
What are the vertex, focus and directrix of a parabola with equation: x = y2 + 14y − 2

Answer 1

the domain is clearly not all real numbers.
Suppose x=0. No way can -9y^2 = 900
The hyperbola is
x^2/900 - y^2/100 = 1
The vertices of the hyperbola are at (±30,0)
So, the domain is (-∞,-30]U[30,∞)
Using what you know of the shape of hyperbolas, the range is clearly all real numbers.

Answer 2

As for the parabola, recall the properties of the parabola
y^2 = 4px
Yours is shifted a bit, making it
(y+7)^2 = 1(x+51)

Answer 3

How did you get the second one?? Also, thank you so much for the first answer. I realized what I was doing wrong lol. I knew how to do it, I was just doing it wrong today