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

1. ## 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).

2. 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

3. 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 $y = ax^2 + bx + c$

Since it passes through (0,3), when x = 0, y = 3. so we have:
$3 = a(0)^2 + b(0) + c = c$................(1)

$\Rightarrow c = 3$, 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:
$4 = a(3)^2 + b(3) + 3$ , since c = 3

$\Rightarrow 9a + 3b = 1$ .....................(2)

Since it passes through (4,11), when x = 4, y = 11. so we have:
$11 = a(4)^2 + b(4) + 3$

$\Rightarrow 16a + 4b = 8$ ....................(3)

So now we have the system:

$9a + 3b = 1$ .................(2)
$4a + b = 2$ ...................(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