Name the pair of vertical angles

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

svetlana [45]

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

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

7 0

3 years ago

Identify the solutions to the quadratic equation.<br> Check all that apply.<br> x2 + 4x - 21 = 0

Vika [28.1K]

Answer:

C and D

Step-by-step explanation:

(X-3)(X+7)=0

X-3=0 X+7=0

X=3 X=-7

8 0

3 years ago

Read 2 more answers

Please help and thank you

Rainbow [258]

Answer:

odp c

Step-by-step explanation:

17*8=136

6 0

3 years ago

A box contains 2 plain pencils and 2 pens. A second box contains 7 color pencils and 3 crayons. One item from each box is chosen

photoshop1234 [79]

In the box containing the 2 plain pencils and 2 pens, there would be a 50% chance of getting a pen. In the other box containing 7 color pencils and 3 crayons there would be a 30% chance of getting a crayon.

8 0

3 years ago

Laura bought a square canvas to paint a picture of her cat one side measured 22 centimeters what is tha area of the canvas

Olin [163]

Hi there!

To start, squares are a shape in which all of its sides are congruent to one another. Knowing the length of one side would mean that you would know the length of all the other sides.

Because you know that one side measures 22 cm, you can conclude that all the other sides of the square are also at a length/width of 22 cm.

Next, you will find the area of the square.

Because the area formula is Area=Length * Width, you can easily find the area of the square by multiplying 22*22 since the length and width of any square is the same.

When you simplify 22*22, you should get 484.

Therefore, the area of the square canvas would be 484 cm squared.

Hope this helps and have a marvelous day! :)

8 0

3 years ago