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
Sholpan [36]
3 years ago
13

at a point P on the parabola x^2=4ay a normal PK is drawn. From vertex O, a perpendicular OM is drawn to meet the normal at M. S

how that the equation of the locus of M as P varies on the parabola is x^4-2ax^2y+x^2y^2-ay^3=0
Mathematics
1 answer:
saveliy_v [14]3 years ago
6 0
<span>Answer: Its too long to write here, so I will just state what I did. I let P=(2ap,ap^2) and Q=(2aq,aq^2) But x-coordinates of P and Q differ by (2a) So P=(2ap,ap^2) BUT Q=(2ap - 2a, aq^2) So Q=(2a(p-1), aq^2) which means, 2aq = 2a(p-1) therefore, q=p-1 then I subbed that value of q in aq^2 so Q=(2a(p-1), a(p-1)^2) and P=(2ap,ap^2) Using these two values, I found the midpoint which was: M=( a(2p-1), [a(2p^2 - 2p + 1)]/2 ) then x = a(2p-1) rearranging to make p the subject p= (x+a)/2a</span>
You might be interested in
Rearrange the formula to make a the subject
PilotLPTM [1.2K]

Answer:

Step-by-step explanation:

p = (3n + a)/(n + a)

Cross multiply

p(n + a) = 3n +a

pn + pa = 3n + a

pa - a = 3n - pn

a(p - 1) = n(3 - p)

Dividing by p - 1

a = n(3 - p)/(p - 1)

7 0
3 years ago
Find the slop that gos through (-8,9) and (-8,-7)​
BaLLatris [955]
The slope is 16/0 which means it is undefined
3 0
2 years ago
As student received a 75% on an exam. If there were 20 questions on the exam which ratio would show the number of questions answ
sergejj [24]
75% times 20=15 so he got 15 correct 
7 0
3 years ago
Read 2 more answers
what interest rate is the local credit union giving you on a car loan of 25,000 for 5 years if they will collect 1500 in interes
lianna [129]

Answer:

1.2%

Step-by-step explanation:

4 0
3 years ago
Pls help I’ll brainlest due ASAP
Sholpan [36]
There is no picture Attached
3 0
2 years ago
Read 2 more answers
Other questions:
  • What is the ratio of the number of cherry slices to the number of orange slices in the medium size bag of candy?
    13·2 answers
  • -49x^2 +16 factor completely
    15·2 answers
  • You are moving the robot to your classroom, which measures 30 feet by 40 feet.
    9·1 answer
  • Jenna is going at a constant rate of 4 miles per hour. It takes her 2 hours to get to her destination. How long would it take to
    15·2 answers
  • F(x) = log3(x + 4)<br> Find<br> f-1(2)
    14·1 answer
  • Smoothie recipe calls for 1/3 cup of bananas. if there are 9/4 cups which statement is true
    13·2 answers
  • What is the measure of an angle that is the supplement of angle K?
    13·1 answer
  • Jett is 6 feet 2 inches tall. How tall is he in inches ?
    15·1 answer
  • Put in least to greatest 3.1 , -3 , -3.75 , 3 1/2 , -3 1/5
    11·2 answers
  • Word Problem On Division
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!