Thread: Conics & Calculus: Conics, Parametric, and Polar Coordinates

Hi, I pealse need an explanation for the following problems. I have no clue..

a)Find the vertex, focus, and directrix of the parabola of the follwing exercices and sketh the graph of the parabola.

1) x^2 +8y = 0

2) (x-1)^2 + 8 (y+2) = 0

3) y^2 + 6y + 8x + 25 = 0


b) Find an equation of parabola of the following exercices

4) vertex: (-1, 2)
focus: (-1,0)

5) focus: (2, 2)
directrix: x= -2

6) When axis is parallel to y-axis; and when graph passes through (0, 3) , (3, 4), and (4, 11).

Originally Posted by googoogaga

Hi, I pealse need an explanation for the following problems. I have no clue..

a)Find the vertex, focus, and directrix of the parabola of the follwing exercices and sketh the graph of the parabola.

1) x^2 +8y = 0

2) (x-1)^2 + 8 (y+2) = 0

3) y^2 + 6y + 8x + 25 = 0


b) Find an equation of parabola of the following exercices

4) vertex: (-1, 2)
focus: (-1,0)

5) focus: (2, 2)
directrix: x= -2

this post may help. it will at least familiarize you with the rules you need to know

Originally Posted by googoogaga

6) When axis is parallel to y-axis; and when graph passes through (0, 3) , (3, 4), and (4, 11).

i'm sure there's an easier way, but i'd probably approach this with simultaneous equations.

Let the desired parabola be of the form

Since it passes through (0,3), when x = 0, y = 3. so we have:
................(1)

, we can use this in the other equations right off the bat, nice!

Since it passes through (3,4), when x = 3, y = 4. so we have:
, since c = 3

.....................(2)


Since it passes through (4,11), when x = 4, y = 11. so we have:


....................(3)


So now we have the system:

.................(2)
...................(3)

Now solve that system and plug in the values for a,b, and c into the form of the quadratic to get your answer