Posted by Anamika on .
In case of parabola
y= x^22x3
Find:
a)Vertex:
b)Axis:
c)Focus:
d)Directrix:
e)Latus Rectum:

maths 
Henry,
Y = x^22x3.
a. h = Xv = B/2A = 2/2 = 1.
K = Yv = 1^22*13 = 4.
V = (h,k) = (1,4).
b. Axis: X = h = 1.
c. D(1,Y1), V(1,4), F(1,Y2).
VF = Y2(4) = Y2+4 = 1/4a = 1/4.
Y2+4 = 1/4.
Y2 = 1/44 = 1/416/4 = 15/4.
d. DV = 4Y1 = 1/4a = 1/4.
4Y1 = 1/4
Y1 = 1/4+4 = 1/4+16/4 = 17/4.
Y1 = 17/4. 
maths 
Henry,
e. A(x1,15/4), F(1,15/4), B(x2,15/4).
AF = 1x1 = 1/2a = 1/2.
1x1 = 1/2.
x1 = 1/21 = 1/2
X1 = 1/2.
FB = x21 = 1/2a = 1/2.
X2 = 1/2+1 = 3/2.
NOTE: The Latus Rectum for the yparabola is a hor. line that passes through the focus.