the length of a rectangular carpet is 2 times it's width. the area is 128 square feet. What is the length?

What is the equation of a parabola with a directrix of y=2 and a focus point of 0,-2

KiRa [710]

Hope this helped. :)

Any point, (x0,y0)(x0,y0) on the parabola satisfies the definition of parabola, so there are two distances to calculate:

Distance between the point on the parabola to the focusDistance between the point on the parabola to the directrix

To find the equation of the parabola, equate these two expressions and solve for y0y0 .

Find the equation of the parabola in the example above.

Distance between the point (x0,y0)(x0,y0) and (a,b)(a,b) :

(x0−a)2+(y0−b)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√(x0−a)2+(y0−b)2

Distance between point (x0,y0)(x0,y0) and the line y=cy=c :

∣∣y0−c∣∣| y0−c |

(Here, the distance between the point and horizontal line is difference of their yy -coordinates.)

Equate the two expressions.

(x0−a)2+(y0−b)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√=∣∣y0−c∣∣(x0−a)2+(y0−b)2=| y0−c |

Square both sides.

(x0−a)2+(y0−b)2=(y0−c)2(x0−a)2+(y0−b)2=(y0−c)2

Expand the expression in y0y0 on both sides and simplify.

(x0−a)2+b2−c2=2(b−c)y0(x0−a)2+b2−c2=2(b−c)y0

This equation in (x0,y0)(x0,y0) is true for all other values on the parabola and hence we can rewrite with (x,y)(x,y) .

Therefore, the equation of the parabola with focus (a,b)(a,b) and directrix y=cy=c is

(x−a)2+b2−c2=2(b−c)y

3 0

3 years ago

Pls help meeeeeeeeeeeeeeeeeeeeeeeeeeee

Dennis_Churaev [7]

1/25 i don’t know if this is right but here you go

5 0

3 years ago

Jimmy is writing a paper for one of his classes. The paper has to be 2000 words long, and so far he has written 532 words. Of he

vova2212 [387]

367 words per day.
Hope this helps!
Vote me brainliest!

3 0

3 years ago

Read 2 more answers

Eddy remembers that the number of a student who liked vanilla was 1/5 of the number who liked almond

anzhelika [568]

I don't really understand this question. But I'll do my best to answer it.
So say that one student liked vanilla, and that student was 1/5 out of kids who liked almond. If that student was the only one out of five students that didn't like vanilla and liked almond, then four more students liked almond, and that one student was left out. So Eddy was right??????

Again, I don't understand what answer you want. Sorry. :/

8 0

3 years ago

The vertices of a triangle are as follows: (4,) (6,7) and (8,0) If you dilate the triangle by a scale factor of 3, what are the

Paraphin [41]

Given:

Consider the vertices of the triangle are (4,4) (6,7) and (8,0).

The triangle is dilated by a scale factor of 3.

To find:

The vertices of the new triangle after dilation.

Solution:

If a figure is dilated by scale factor k with origin as the center of dilation, then the rule of dilation is:

$(x,y)\to (kx,ky)$