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
Mrac [35]
3 years ago
8

What is the equation of the quadratic graph with a focus of (3, 6) and a directrix of y = 4? f(x) = one fourth (x − 3)2 + 1 f(x)

= one fourth (x − 3)2 + 5 f(x) = −one fourth (x − 2)2 + 5 f(x) = −one fourth (x − 2)2
Mathematics
1 answer:
mina [271]3 years ago
8 0
 Let point (x, y) be any point on the graph, than the distance between (x, y) and the focus (3, 6) is sqrt((x - 3)^2 + (y - 6)^2) and the distance between (x, y) and the directrix, y = 4 is |y - 4|

Thus sqrt((x - 3)^2 + (y - 6)^2) = |y - 4|
(x - 3)^2 + (y - 6)^2 = (y - 4)^2
x^2 - 6x + 9 + y^2 - 12y + 36 = y^2 - 8y + 16
x^2 - 6x + 29 = -8y + 12y = 4y
(x - 3)^2 + 20 = 4y
y = 1/4(x - 3)^2 + 5

Required answer is f(x) = one fourth (x - 3)^2 + 5
You might be interested in
Two similar cylinders have radii of 15 inches and 6 inches. What is the ratio of the surface area of the small cylinder to the s
Levart [38]

Answer:

4:25

Step-by-step explanation:

Given that,

r₁ = 15 inches, r₂ = 6 inches

The area of the cylinder is given by :

A=2\pi rh+2\pi r^2

The ratio of surface areas of two cylinders,

\dfrac{S_2}{S_1}=\dfrac{2\pi r_2h_2+2\pi r_2^2}{2\pi r_1h_1+2\pi r_1^2}\\\\\dfrac{S_2}{S_1}=(\dfrac{r_2}{r_1})^2\\\\=\dfrac{6}{15}^2\\\\=\dfrac{4}{25}

Hence, the required ratio is 4:25.

8 0
3 years ago
A car travels 17 miles on one gallon of gas.
Margarita [4]

Answer:

y*17x

Step-by-step explanation:

y is a gallon so LEARN!

7 0
3 years ago
△PQR has two known interior angles of 34°, and 80°. △RST has two known interior angles of 24°, and 90°. What can be determined a
Nonamiya [84]
B.the triangles are not similar
7 0
3 years ago
What system of linear inequalities is shown in the graph?
NARA [144]
The first one i think
5 0
3 years ago
Which of the following equations have a solution of y = -22 ? Select all that apply.
nevsk [136]

Answer:

Where are the equations?

7 0
3 years ago
Other questions:
  • Carter is playing a video game he needs to score more than a hundred points to move on to the next level write an inequality to
    15·1 answer
  • <img src="https://tex.z-dn.net/?f=6%20%2B%20%20%5Cfrac%7Bv%7D%7B%20-%208%7D%20%20%3D%20%20%5Cfrac%7B4%7D%7B7%7D%20" id="TexFormu
    11·1 answer
  • A lender is charging 2.75 points on a $275,000 loan. The borrower must therefore pay the lender an advance amount of $11,000? $6
    13·2 answers
  • (07.08 LC) The table below shows the values of y for different values of x: Which equation shows the relationship between x and
    6·1 answer
  • Select the correct answer.
    15·1 answer
  • Which best states George Washington’s connection to the 1787 Constitutional Convention? He was an honorary delegate because he h
    5·2 answers
  • A company’s stock was selling at $28 a share.A month later , it was selling at $21 a share.What is the percent loss
    9·1 answer
  • If 4/3 liters of water are enough to water 2/5 of the plants in the house, how som:
    6·2 answers
  • If the measure of arc AB is 50 degrees, what is the measure of angle ADB
    15·1 answer
  • Write the expression as the sine or cosine of an angle<br> pi/5 cos pi/2+sin pi/2\cos pi/5
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!