An s w e r q u i c k p l e a s e

1. the directrix of a parabola is y=−8 . the focus of the parabola is (−2,−6) .

what is the equation of the parabola?

y=14(x+2)2−7

y=−18(x+2)2+7

y=18(x−2)2−7

y=−14(x−2)2−7

2. the directrix of a parabola is the line y=5 . the focus of the parabola is (2,1) .

what is the equation of the parabola?

y=−18(x−2)2−3

y=18(x−2)2+3

y=18(x−2)2−3

y=−18(x−2)2+3

3. the focus of a parabola is (0,−2) . the directrix of the parabola is the line y=−3 .

what is the equation of the parabola?

y=14x2−2

y=−12x2−52

y=−14x2+2

y=12x2−52

1. A

2. D

3. D

Step-by-step explanation:

The standard form of a parabola is

           ..... (1)

Where, (h,k) is vertex, (h,k+p) is focus and y=k-p is directrix.

1. The directrix of a parabola is y=−8 . The focus of the parabola is (−2,−6) .

                  ...(a)

           .... (b)

On solving (a) and (b),  we get k=-7 and p=1.

Put h=-2, k=-7 and p=1 in equation (1).

Therefore option A is correct.

2 The directrix of a parabola is the line y=5 . The focus of the parabola is (2,1) .

                  ...(c)

           .... (d)

On solving (c) and (d),  we get k=3 and p=-2.

Put h=2, k=3 and p=-2 in equation (1).

Therefore option D is correct.

3. The focus of a parabola is (0,−2) . The directrix of the parabola is the line y=−3 .

                  ...(e)

           .... (f)

On solving (e) and (f),  we get k=-2.5 and p=0.5.

Put h=0, k=-2.5 and p=0.5 in equation (1).

Therefore option D is correct.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

2

step-by-step explanation: