Answer:
(x²-10x+33)/(-8) = y
Step-by-step explanation:
The distance between any point on a parabola from both its focus and directrix are the same.
Let's say we have a point (x,y) on the parabola. We can then say that using the distance formula,
is the distance between (x,y) and the focus. Similarly, the distance between (x,y) and the directrix is |y-1| (I use absolute value here because distance is always positive). We can find this equation by taking the shortest distance from the point to the line. Because the closest point to the line will be the same x value as the point itself, the distance is simply the distance between the y value of the point and the y value of the directrix.
Equating the two equations given, we have
square both sides to get
(x-5)²+(y+3)²=(y-1)²
expand the y components
(x-5)² + y²+6y+9 = y²-2y+1
subtract y²+6y+9 from both sides
(x-5)² = -8y - 8
expand the x components
x²-10x+25 = -8y - 8
add 8 to both sides to isolate the -8y
x²-10x+33 = -8y
divide both sides by -8 to isolate y
(x²-10x+33)/(-8) = y
Answer:
huh okay well hi
Step-by-step explanation:
may the force be with u :)
Answer:
Step-by-step explanation:
Let's assume that you have a sequence written out in always increasing or always decreasing order.
If each new term is equal to the previous term, plus a certain constant, then the sequence is arithmetic. Example: 2, 7, 12, 17, 22, ... (the additive constant is 5).
If each new term is equal to the previous term, multiplied by a certain constant, then the sequence is geometric. Example: 2, 8, 32, 128, ... (the multiplicative constant is 4).
If the spacing between terms is not a constant, then the sequence is neither arith. nor geom.
If all new adjacent terms are not found by multiplying the previous term by the same constant, the sequence is not geometric (and not arithmetic).
