Two parabolas have the same focus, namely the point $(3,-28).$ their directrices are the $x$-axis and the $y$-axis, respectively. compute the slope of their common chord.

the slope of the common cord is:

Step-by-step explanation:

Given the focus (a,b) = (3,-28)

The common chord is the line between two points where the two parabolas intersect. For intersection, we can equate the two parabolas!

In other words, at the point of intersection of these two parabolas the values of the two parabolas will be the same.

we can now simplify the equation. (we can see that (x-3) and (y+28) both cancel out by -(x-3) and -(y+28))

this the equation of the common cord. but we need to select whether its

or .

This can be found by realizing that the focus lies on the 4th quadrant of the xy-plane! And the equation also generates a line that exists in the 2nd and 4th quadrant.

Hence the slope of the common cord is the slope of the line

that is :

the third picture

step-by-step explanation:

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3