maths

posted by .

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.

Similar Questions

1. Pre Cal

write the equations of the parabola, the directrix, and the axis of symmetry. vertex: (-4,2) focus: (-4,6) if someone could explain how to do this problem then that would be great! thanks in advance! Formats to help you find the equation …
2. algebra 2

Find the vertex, focus, axis, directrix and latus rectum of the parabola x^2+ y = 6x - 14
3. algebra

6. Find the equation of each parabola described below. a) parabola with vertex (0,0) and the focus (0,7) b) parabola with focus (-3,0) and directrix x=3 c) parabola with vertex (3,3) and directrix x=-1 d) parabola with focus (-2,-1) …
4. Trig: Conics

Sketch the graph and find following info: Vertex: Focus: Directrix: Axis of Symmetry: Ends of Latus Rectum: (x-2)^2=4(y-3) I think the vertex is (2,3) is this correct, and how do I proceed on?
5. math

if equation of directrix of a parabola is 2x+3=0, axis is 2y-3=0 and length of latus rectum is 6 then what will be the focus?
6. maths

Given that the equation of the parabola is 5y^2 + 24x = 0. Find (1)The Axis and vertex of the parabola (ii)The focus and the directrix (iii)The distance from the directrix to the focus
7. Analytic Geometry

A parabola has a directrix y=-3, axis =4 and latus rectum equal to 2. find its equation. Please help me its for my homework
8. analytic geometry

1. Given the parabola defined by y^2 = -12x, find the coordinates of the focus, the length of the latus rectum and the coordinates of its endpoints. Find also the equation of the dielectric. Sketch the graph. 2. Find the eccentricity …
9. analytic geometry

1. Given the parabola defined by y^2 =-12x, find the coordinates of the focus,the length of the latus rectum and the coordinates of its endpoints.Find also the equation of the directrix. Sketch the curve. 2. Find the eccentricity of …
10. Pre calc

Find an equation of the parabola described and state the two points that define the latus rectum Focus at (0,4) ; Directrix the line y=4

More Similar Questions