MATH SOLVE

3 months ago

Q:
# Find the equation of the parabola with a focus (2, 5) and directrix of y = 3.A.)y=x^2/4 + x + 5B.)y=x^2/4 + x -5C.)y=x^2/4 -x - 5D.)y=x^2/4 - x + 5

Accepted Solution

A:

Answer:
One form of an equation is given by Β y=a(xβh
)
2
+k
y=a(xβh)2+k
where Β (h,k)
(h,k)
the coordinates of the vertex and Β (h,k+
1
4a
)
The parabola is symmetric with respect to Β y=x
y=x
and can be viewed as a standard downward parabola with a rotation of 45 degrees clockwise. So, follow the steps below to obtain its equation.
1) The length between the focus and vertex is Β f=
4
2
+
4
2
β
β
β
β
β
β
β
=4
2
β
β
f=42+42=42
. The standard equation is Β y=β
1
4f
x
2
y=β14fx2
.
2) Shift the vertex to (-2, -2),
y+2=β
1
16
2
β
β
(x+2
)
2
y+2=β1162(x+2)2
3) Rotate the equation -45-degrees Β xβ
1
2
β
(xβy)
xβ12(xβy)
, Β yββ
1
2
β
(x+y)
yββ12(x+y)
to get
β
1
2
β
β
(x+y)+2=β
1
16
2
β
β
(
1
2
β
β
(xβy)+2)
2
Step-by-step explanation: