Question

I will give MEDAL!!

Answer 1

A)find center and radius of -x^2+y^2+4y-16=0
B) Find vetex x^2+x-y-42=0

Answer 2

@phi @zepdrix @ZeHanz

Answer 3

If A is supposed to be a circle, then I think the equation should read x^2+y^2+4y-16=0, so without the minus before x^2.

Answer 4

Leave the x² alone.
Let's look at y²+4y.
It looks like the expanded form of (y+2)² = y²+4y+4.
So y²+4y=(y+2)²-4.

Now we put everything back in the equation:

x²+(y-2)²-4-16=0, or: x²+(y-2)²=20

I think you know this general form of the circle equation:

(x-a)²+(y-b)²=r². It is a circle with midpoint (a, b) and radius r.

If you compare it with what we found: x²+(y-2)²=20, I'm sure you can work out a, b and r!

Answer 5

B is a parabola, and it is more convenient to write it as : y=x²+x-42.

In the general formula for such a parabola:

y=ax²+bx+c,

the x-coordinate of the vertex is -b/(2a).

Because I have written the equation in that standard form, you can read the values of a and b, so that gives you the x-coordinate of the vertex.
Put that x in the equation to find the y-coordinate.