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maths

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

  • maths - ,

    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.

  • maths - ,

    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.

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