Sketch the graph of the following parabolas. Identify the...

Sketch the graph of the following parabolas. Identify the coordinates of the vertex, focus, end points of latus rectum and determine the equations of the directrix and axis of symmetry. Find the x and y- intercepts. 1. (x + 2)^2 = 4(y - 3) 2. y^2 - 12x + 4y + 52 = 0

Transcript

00:01 This is a parabola, but it is not exactly the standard parabola.

00:06 So what we do is let small x plus 2, we'll call it as capital x and small y minus 3 is quality as capital y.

00:15 So capital x is equal to 4y, which is a standard parabola.

00:19 Now, if you draw capital x axis and capital y axis, this parablea looks something like this.

00:25 This is the parabola.

00:26 The vertex of this parabola is origin.

00:29 The vertex is origin but what will be the vertex of this parabola so origin means capital x is zero capital y is zero convert back to small x and small y so small x plus 2 is 0 small y minus 3 is 0 so the vertex of this parabola is x is negative to y is negative 2 comma 3 is the vertex and what is the focus of this parabola the focus of this parabola is actually the focus of the parabola x square is equal to 4a y is 0 comma a is the focus this is the focus so here is 0 comma 1 because a is 1 here because 4 into 1 is 4.

01:04 So that means capital x is 0 capital y is 1.

01:07 So that means small x is equal to negative 2 whereas y is equal to 4.

01:12 So the focus of this parabola is negative 2 comma 4 is the focus.

01:16 This is the focus of the parabola.

01:19 Now the directrix of the parabola, the directrix is given by the equation capital x is equal to negative a negative a here is 1.

01:26 Capital x is equal to negative 1.

01:28 But capital x is small x plus 2.

01:30 So small x plus 2 is equal to negative 1 means x is equal to negative 3.

01:33 This is the equation of the directrix.

01:37 So this is the directrix.

01:39 X is equal to minus 3 squared directs.

01:42 Sorry, this is the directrix.

01:44 Now what is the latest rectum? the latest rectum as two end points.

01:50 So for this parabola, x squared is equal to 4 y.

01:52 The latest rectum will be sitting here.

01:54 Sorry, it will be parallel to x axis and then passing to 4.

01:59 This is the latest rectum line segment.

02:01 So it's a coordinates are basically for this parable are the coordinates will be 2a, 2a comma a here and negative 2a comma a here.

02:12 But in this case, a is one right? so what are the latest rectum endpoints of capital x square is equal to 4y? it is negative 2 comma 1 and 2 comma 1.

02:23 But capital x is equal to negative 2 here, capital y is 1 here, whereas here capital x is 2 capital y is equal to 1 but capital x is what small x plus 2 so small x plus 2 is negative 2 here and capital y is what small y minus 3 is equal to 1 here here small x plus 2 is equal to 2 and y minus 3 is equal to 1 so that if you calculate is minus 4 comma 4 is 1 point of the latest rectum here and 0 comma 4 is the other end point of the latest spectrum so these are the end points of the latest rectum or lr endpoints alarm lr end points lr means latest rectum all right so that is the latest spectrum directics we have completed vertex we have completed focus we have completed axis of symmetry the axis of symmetry for this parabola x square equal to 4 y is y axis so capital x is equal to 0 so what will be the axis of symmetry for main parabola capital x is what small x plus 2 is equal to negative 2 so x is equal to negative 2 is the axis of symmetry aos aos means of symmetry.

03:30 Next, we have to find x and y intercepts...

Question

Sketch the graph of the following parabolas. Identify the coordinates of the vertex, focus, end points of latus rectum and determine the equations of the directrix and axis of symmetry. Find the x and y- intercepts. 1. (x + 2)^2 = 4(y - 3) 2. y^2 - 12x + 4y + 52 = 0

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