name vertex, focus, direction of opening, diretrex, axis of symmetry.?

Question

(x-1)² = 12(y-1)

Answer 1

On comparing the standard equation of parabola
4a(y - k) = (x - h)²

h = 1
k = 1
4a = 12 => a = 3

The x² and y terms are on opposite sides and have the same sign so it opens upward.
The vertex is (h, k) i.e.
(1, 1)

The focus is inside the parabola at a vertical distance a from the vertex. So the focus is at (h, k + a). i.e.
(1, 4)

The axis of symmetry is a line thru the vertex and focus. The equation of the line is: x = h i.e.
x = 1

The directrix is perpendicular to the axis of symmetry and is the distance p from the vertex in the opposite direction of the focus. It is outside the parabola. Its equation is y = k – a i.e.
y = 1 – 3
y = -2

Answer 2

This is the equation of a parabola. If you have a parabola opening vertically you can write the equation as:

4p(y - k) = (x - h)²

x is the squared term so it opens vertically.

The x² and y terms are on opposite sides and have the same sign so it opens upward.

The vertex is (h,k).

The focus is inside the parabola at a vertical distance p from the vertex. So the focus is at (h,k+p).

The axis of symmetry is a line thru the vertex and focus. The equation of the line is:

x = h

The directrix is perpendicular to the axis of symmetry and is the distance p from the vertex in the opposite direction of the focus. It is outside the parabola. Its equation is

y = k - p
__________________

Apply these principles and you should be able to answer the question.

Answer 3

general eqn is (x-h)^2 = 4a(y-k)

here a=3,h=1,k=1

vertex = (h,k)=(1,1)
focus=(h,a+k) = (1,4)
direction of opening = towards positive y axis
directrix is y= -a+k ; y =-2 ==> y+2 =0
axis of symmetry, x=h; x=1 ==> x-1=0

Answer 4

wide-spread eqn is (x-h)^2 = 4a(y-ok) the following a=3,h=a million,ok=a million vertex = (h,ok)=(a million,a million) concentration=(h,a+ok) = (a million,4) route of starting off = in the route of effective y axis directrix is y= -a+ok ; y =-2 ==> y+2 =0 axis of symmetry, x=h; x=a million ==> x-a million=0

Answer 5

(x-1)^2=12(y-1)
Vertex=(1,1)
general form-X^2=4AY
X=x-1
Y=y-1
A=3
focus=(1,4)
it opens upwards
Axis of symmetry-x=1