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
Ksivusya [100]
3 years ago
11

The equation of the tangent plane to the ellipsoid x2/a2 + y2/b2 + z2/c2 = 1 at the point (x0, y0, z0) can be written as xx0 a2

+ yy0 b2 + zz0 c2 = 1 Find the equation of the tangent plane to the hyperboloid x2/a2 + y2/b2 − z2/c2 = 1 at (x0, y0, z0) and express it in a form similar to the one for the ellipsoid.
Mathematics
1 answer:
svetlana [45]3 years ago
7 0

Answer:

The equation of tangent plane to the hyperboloid

\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=1.

Step-by-step explanation:

Given

The equation of ellipsoid

\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1

The equation of tangent plane at the point \left(x_0,y_0,z_0\right)

\frac{xx_0}{a^2}+\frac{yy_0}{b^2}+\frac{zz_0}{c^2}=1  ( Given)

The equation of hyperboloid

\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1

F(x,y,z)=\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}[c^2}

F_x=\frac{2x}{a^2},F_y=\frac{2y}{b^2},F_z=-\frac{2z}{c^2}

(F_x,F_y,F_z)(x_0,y_0,z_0)=\left(\frac{2x_0}{a^2},\frac{2y_0}{b^2},-\frac{2z_0}{c^2}\right)

The equation of tangent plane at point \left(x_0,y_0,z_0\right)

\frac{2x_0}{a^2}(x-x_0)+\frac{2y_0}{b^2}(y-y_0)-\farc{2z_0}{c^2}(z-z_0)=0

The equation of tangent plane to the hyperboloid

\frac{2xx_0}{a^2}+\frac{2yy_0}{b^2}-\frac{2zz_0}{c^2}-2\left(\frac{x_0^2}{a^2}+\frac{y_0^2}{b^2}-\frac{z_0^2}{c^2}\right)=0

The equation of tangent plane

2\left(\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}\right)=2

Hence, the required equation of tangent plane to the hyperboloid

\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=0

You might be interested in
CAN SOMEONE PLEASE HELP ME WITH THIS!! ILL GIVE YOU BRAINLIST ANSWER <br> IMAGE DOWN BELOW!
Basile [38]

how long is |MN| when you measure it and do you know anything about the length of |NO| and |OP|?

assuming |MN|= 7.7 ; |NO|= 4.7 ; |MO|= 5.5:

o²= m²+n²

= 4.7²+5.5²

=52.34

o=V52.34

≈7.23

5 0
2 years ago
Write a program that will enable Tracy to draw one circle with a diameter of 50
e-lub [12.9K]

Answer:

circle(50)

Step-by-step explanation:

The circle should have a diameter of 50 so the answer is simply "circle (50)"

8 0
2 years ago
There is 30 points to whoever can figure this out
Nostrana [21]
I don’t really know….but nice computer :)
5 0
2 years ago
Which number line would best model the quotient 3/4 divided by 6?​
slava [35]
I think it’s D I hope this helps!!!
6 0
2 years ago
What is the value of 6\7 = ?
Sergio039 [100]
It is roughly 0.857 in decimal or in fractions 6/7.  Please mark Brainliest!!!
4 0
3 years ago
Other questions:
  • 9 to the 12th power divided by 9 to the 8th power
    9·1 answer
  • A poster is shown below: A rectangle is shown. The length of the rectangle is labeled 12 feet. The width of the rectangle is lab
    6·2 answers
  • The functions f(x) and g(x) are shown below:
    10·2 answers
  • 5 divided by what number equals 30
    5·2 answers
  • Neena is listening to a song. It has a consistent beat. She counts 11 beats in
    15·1 answer
  • Pls help asap Its due in 10 min pls help
    11·1 answer
  • How much lace does she uses for he jewel box?
    15·1 answer
  • ¿que tipo de par ordenado es Veracruz-jalapa? ​
    14·1 answer
  • Help please, try to explain it in steps for me if u can't that's fine, ty!
    10·1 answer
  • Do long division for each fraction ✔️
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!