Problem of the Day
Find the equation of the circle
1. (­2,­3) r = 4
2. (0, 6) r = 1
3. (0,0) r = Mr. Stalter is far sighted. What does that mean?
Problem of the Day
Find the focus and directrix of the equation.
1. (y­4)2 = ­2x
2. (x+1)2= ­16(y ­ 3)
Problem of the Day
Find the focus and directrix of the equation.
1. (x­2)2= ­12(y + 2)
Problem of the Day
Graph the parabola with equation (y + 1)2 = ­8(x ­ 2). Find the focus and directrix.
Standard form of a Parabola
y = x2 ­ 4x ­ 5
Things to Remember
Conic Sections: Parabola
Standard Equations of Parabolas(Vertex Form)
1. (x­h)2 = 4a(y­k)
Vertex (h,k)
Focus Directrix: Axis of Symmetry: (vertical line of symmetry)
2. (y­k)2 = 4a(x­h) Vertex (h,k)
Focus Directrix: Axis of Symmetry: (vertical line of symmetry)
Find the focus and directrix of (x+1)2 = ­16(y­2). Then graph the equation.
Find the focus and directrix of (y­3)2 = 8(x+2). Then graph the equation.
Practice Problems
Graph the parabola with equation (x + 2)2 = ­8(y ­ 3). Find the vertex, focus, directrix, and axis of symmetry.
Practice Problems
Graph the parabola with equation (y + 5)2 = ­2(x ­ 1). Find the vertex, focus, directrix, and axis of symmetry.
Find the equation of the parabola where the vertex is (­3,4) and (­10,­5) is on the graph. The axis of symmetry is x = ­3. Find the coordinates of the focus and the equation of the directrix.
Find the vertex, focus and directrix of the parabola with the equation(complete the )
y2 = 8x ­ 12y ­ 4
x2 ­ 8x + 4y = 0
Find the equation of a parabola having (­1,­2) as its vertex, the line y = ­2 as the axis of symmetry, and (4,­8) is on the graph. Find the coordinates of the focus and equation of the directrix.
Practice Problems
Write the equation of the parabola with focus (­3,0) and directrix equation y = 6.
Write the equation of the parabola with directrix y = 4 and vertex at the origin.
More Practice Problems
Write the equation of the parabola whose vertex is (0,4), axis of symmetry is the y­axis and passes through the point (­6,­3)
Write the equation of the parabola whose directrix is x = ­5 and focus at (­1, 6)
Find the vertex and focus of the parabola with the following equation.
4x = y2 ­ 10y ­ 3 Vertex(­7,5)
Focus(­6,5)
Directrix x = ­8
Vertex(­1,­1) and directrix y = 0
Vertex (­4,­2), axis of symmetry is x = ­4, and passes through (­5,­12)
Practice Problems
Assume the vertex is the origin.
Find the focus and directrix of the parabola that is symmetrical to the y­axis and contains the point (­1,2)
Find the center and radius of the circle.
x2 + y2 ­ 16x + 15 = 0
The circle with a diameter with endpoints at (2, ­3) and (6, 0)