Derive the equation of the parabola with a focus at (-5, 5) and a directrix of y = -1. (2 points) Please help

1 answer:

4 0

We see that the the parabola opens up since directix is below the focus

for an parabolla opening up/down with vetex at (h,k) and the distance from teh vertex to the focus is p
$(x-h)^2=4p(y-k)$
the distance from vertex to directex is the same as from focus to directix

from (-5,5) and y=-1
that is a vertical distance of 6
vertex is in the middle
6/2=3
5-3=2
the vertex is at (-5,2)
the distance is 3
$(x-(-5))^2=4(3)(y-(2))$
$(x+5)^2=12(y-2)$
$y=\frac{1}{12}(x+5)^2+2$

You might be interested in

The following sequence has first five terms as: -20, -17, -14, -11, -8, .......... Find an expression for the nth term of the se

Maslowich

Answer:

a(n) = -20 + 3(n - 1)

Step-by-step explanation:

a(n) = -20 + 3(n - 1)

4 0

2 years ago

Hi, the answer is K but can anyone show why

dlinn [17]

Let's do 51 and 52.

51. The contrapositive has the same truth value as the original statement. That's opposed to the converse, which may or may not be true independent of the original statement.

The contrapositive of IF P THEN Q is IF not Q THEN not P. They're equivalent. Here that's If the cat is not female then it is not tricolor.

Answer: C

52.

$(x^3)^{(4-b^2)}=1$

$x^{3(4-b^2)} = 1$

For the statement to be true, the exponent must be zero:

$3(4-b^2) = 0$

$b^2 = 4$

$b = \pm 2$

Both positive 2 and negative 2 have a square of 4.

Answer: K

By the way, usually we assume $0^0=1$ so the restriction that $x \ne 0$ isn't really necessary. Think of the definition of a polynomial or the binomial expansion: