1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anastasy [175]
3 years ago
14

Which equation represents the equation of the parabola with focus (-3 3) and directrix y=7?

Mathematics
1 answer:
Artemon [7]3 years ago
6 0

Answer:

The equation y=\frac{-x^2-6x+31}{8} represents the equation of the parabola with focus (-3, 3) and directrix y = 7.

Step-by-step explanation:

To find the equation of the parabola with focus (-3, 3) and directrix y = 7. We start by assuming a general point on the parabola (x, y).

Using the distance formula d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }, we find that the distance between (x, y) is

\sqrt{(x+3)^2+(y-3)^2}

and the distance between (x, y) and the directrix y = 7 is

\sqrt{(y-7)^2}.

On the parabola, these distances are equal so, we solve for y:

\sqrt{(x+3)^2+(y-3)^2}=\sqrt{(y-7)^2}\\\\\left(\sqrt{\left(x+3\right)^2+\left(y-3\right)^2}\right)^2=\left(\sqrt{\left(y-7\right)^2}\right)^2\\\\x^2+6x+y^2+18-6y=\left(y-7\right)^2\\\\x^2+6x+y^2+18-6y=y^2-14y+49\\\\y=\frac{-x^2-6x+31}{8}

You might be interested in
What is third of 1 2/3
arlik [135]

Answer:

5/9

Step-by-step explanation:

1/3 * 1 2/3

1/3 * 5/3

5/9

8 0
3 years ago
Read 2 more answers
Can someone please help me ASAP​
deff fn [24]

Answer:

QR = 17 cm

Step-by-step explanation:

Δ RST is a 5- 12- 13 triangle with hypotenuse RT = 13 cm , then

TS = 5 cm and PT = 2 × 5 = 10 cm

So PS = 10 + 5 = 15 cm

PS is parallel to the vertical line from vertex Q and intersects the horizontal line projected from SR of length 20 - 12 = 8 cm

Using the right triangle formed calculate QR using Pythagoras' identity

QR² = 15² + 8² = 225 + 64 = 289 ( take square root of both sides )

QR = \sqrt{289} = 17

3 0
3 years ago
I
Delvig [45]

Answer:

y= 1/2 x +7

the slope is 1/2 since hwne it's perpendicular, it's reciprocal and the sign also changes

Step-by-step explanation:

3= -4 +b

b= 7

4 0
2 years ago
What is 2x-9y=14 need immediate help​
Vinvika [58]

Let's solve for x.

2x−9y=14

Step 1: Add 9y to both sides.

2x−9y+9y=14+9y

2x=9y+14

Step 2: Divide both sides by 2.

2x /2

= 9y+14 /2

x= 9 /2 y+7

5 0
3 years ago
Read 2 more answers
A ball bounces three-fourths the height of its fall. the ball bounces 12ft.,how high does it bounce on the first bounce?
Fynjy0 [20]
16 feet is the answer to your question
8 0
3 years ago
Other questions:
  • How to simplify 14+5(x+3)-7x
    5·2 answers
  • Please help me
    13·2 answers
  • If a point ,located at (3,-2),is rotated clockwise 90 about the origin,what are the coordinates of its image ’?
    15·1 answer
  • Help plzzzzzzzzzzzzzz
    10·1 answer
  • 3*4-1*2 simplest form
    10·1 answer
  • HELP PLEASE!!! What is the volume of this container?
    15·1 answer
  • In a given amount of time, Mary drove twice as far as Lynn. Altogether they drove 60 miles. How far did Mary
    7·1 answer
  • The equation below describes a proportional relationship between x and y. What is the constant of proportionality? y = 2/9x
    9·1 answer
  • Jermaine is saving $60 per week for a new guitar. The amount he has saved, s, is represented by
    5·1 answer
  • A motorboat travels 275 kilometers in 5 hours going upstream. It travels 405 kilometers going downstream in the same amount of t
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!