pLease show me how to do this??

Question

anonymous · Answer

attachment

ganeshie8 · Answer

notice that focus is 6 units away from the vertex

ganeshie8 · Answer

for part a) :
1) Focus is 6 units away from the vertex
2) the parabola opening up

ganeshie8 · Answer

for part b) :
if we assume the vertex is at (0, 0), then :
1) the coordinates of Focus will be $(0, 6)$
2) the equation of Directrix will be $y = -6$

ganeshie8 · Answer

can u write the equaiton of parabola wid that info ha ?

anonymous · Answer

no....:(

ganeshie8 · Answer

its bit easy, do u knw distance formula ?

ganeshie8 · Answer

say $(x, y)$ is some point on parabola, then by definition of parabola, this point is equidistant to both Focus and Line :

$\sqrt{(x-0)^2 + (y-6)^2} = y--6$

ganeshie8 · Answer

square both sides and simplify

ganeshie8 · Answer

say $(x, y)$ is some point on parabola, then by definition of parabola, this point is equidistant to both Focus and Line :

$\sqrt{(x-0)^2 + (y-6)^2} = y--6$

$x^2 + (y-6)^2 = (y+6)^2$

$x^2  - 12y = 12y$

$x^2   = 24y$

$y = \frac{1}{24}x^2$

ganeshie8 · Answer

thats the required equation of parabola

ganeshie8 · Answer

see if that makes more or less sense

anonymous · Answer

is that all I do?

ganeshie8 · Answer

yes, but make sure u understand how the equation was derived lol

anonymous · Answer

THANKYOU

ganeshie8 · Answer

its just application of distance formula, if u go thru it u wil find it easy im sure... give it a try ok