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
Margaret [11]
3 years ago
12

Two curves are orthogonal if their tangent lines are perpendicular at each point of intersection. are the given families of curv

es orthogonal trajectories of each other? that is, is every curve in one family orthogonal to every curve in the other family? x2 + y2 = ax x2 + y2 = by
Mathematics
1 answer:
Akimi4 [234]3 years ago
5 0
Hello,

P(x,y)=x^2+y^2-ax=0\\\\
\dfrac{\partial{P}}{\partial{x}}=2x-a\\\\
\dfrac{\partial{P}}{\partial{y}}=2y\\\\


Q(x,y)=x^2+y^2-by=0\\\\
\dfrac{\partial{Q}}{\partial{x}}=2x\\\\
\dfrac{\partial{Q}}{\partial{y}}=2y-b\\\\

\dfrac{\partial{P}}{\partial{x}}*\dfrac{\partial{Q}}{\partial{x}}+\dfrac{\partial{P}}{\partial{y}}*\dfrac{\partial{Q}}{\partial{y}}=(2x-a)*2x+2y(2y-b)\\
=4x^2+4y^2-2ax-2by\\
=2(2x^2+2y^2-ax-by)\\
=2*P(x,y)+Q(x,y))\\
=2*(0+0)=0\\\\

Answer YES

You might be interested in
malinda must take30 cubic centimeters of her medicine every 6 hours.how many milliliters are equivalent to 30 cubic centimeters
NikAS [45]

Answer:

30 milliliters

Step-by-step explanation:

multiply the volume value by 1

6 0
3 years ago
Write an equation in slope-intercept form of the line that passes through (-1,4) and (0,2).
ratelena [41]

Answer:

1,3

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Solve 2x – 6y = 4 for x.
MArishka [77]

Answer:

A

Step-by-step explanation:

bro how come u dont answer for yourself? The point of school is for you to learn. . . but anyway the answer is A

5 0
3 years ago
Find the surface area of the prism. 7yd 7yd 7yd.
Alekssandra [29.7K]

Answer:

294 yd ^2

Step-by-step explanation:

it should be correct!

3 0
3 years ago
Read 2 more answers
What Is 4/14 in simplest form?
Natali [406]
The answer I believe it will be 2/7 I think
8 0
3 years ago
Other questions:
  • 1. Find a unit vector that is orthogonal to both u and v.
    15·1 answer
  • Find the difference between 45 2/3 and 27 1/2 . Express your answer in lowest terms
    11·1 answer
  • What is y=21 times 8×34
    14·1 answer
  • Can someone awnser this question please? -6+[10:(4+5)]+7=​
    9·1 answer
  • Pls help asap! Will give brainliest
    10·2 answers
  • They are terrible with providing contented needed before hand Big help thanks
    7·1 answer
  • Rewrite the following expression using only addition: 4x-2y-8
    11·1 answer
  • Y
    14·1 answer
  • Write an equation of the line that passes through the given points.<br> (-1,7) and (4, -8)
    6·1 answer
  • C
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!