Question

In case of parabola
y= x^2-2x-3
Find:
a)Vertex:
b)Axis:
c)Focus:
d)Directrix:
e)Latus Rectum:

Answer 1

Y = x^2-2x-3.

a. h = Xv = -B/2A = 2/2 = 1.
K = Yv = 1^2-2*1-3 = -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 = 1/4-4 = 1/4-16/4 = -15/4.

d. DV = -4-Y1 = 1/4a = 1/4.
-4-Y1 = 1/4
-Y1 = 1/4+4 = 1/4+16/4 = 17/4.
Y1 = -17/4.

Answer 2

e. A(x1,-15/4), F(1,-15/4), B(x2,-15/4).

AF = 1-x1 = 1/2a = 1/2.
1-x1 = 1/2.
-x1 = 1/2-1 = -1/2
X1 = 1/2.

FB = x2-1 = 1/2a = 1/2.
X2 = 1/2+1 = 3/2.

NOTE: The Latus Rectum for the y-parabola is a hor. line that passes through the focus.