# Equation of tangent plane

• Jan 30th 2010, 01:48 PM
rain21
Equation of tangent plane
Find the equation of the plane tangent to the graph of the function

z(x,y) = 7(x^2) − 6(y^2) − 7x + 4y + 7 at the point (x,y)=(9,9)

the z(x,y) is throwing me off since it isnt f(x,y). Is there any difference?

I've done this problem about a million time, and am still not getting the right answer.

my solution:
\$\displaystyle z_x = 14x - 7 \$
\$\displaystyle z_x (9,9) = 14(9) - 9 = 119 \$

\$\displaystyle z_y = -12y + 4 \$
\$\displaystyle z_y = -12(9) + 4 = -104 \$

there is no value for z though which confuses me.

I know that an equation of the tangent plane to the surface z = f(x,y) at the point \$\displaystyle P (x_0, y_0, z_0) \$ is
\$\displaystyle z-z_0=f_x (x_0 ,y_0 )(x-x_0 ) + f_y (x_0, y_0)(y-y_0) \$

but when I plug in everything into this equation I get \$\displaystyle z = 119(x-9) - 104(y-9) \$ which is wrong. Any help would be appreciated.
• Jan 30th 2010, 03:42 PM
General
Quote:

Originally Posted by rain21
Find the equation of the plane tangent to the graph of the function

z(x,y) = 7(x^2) − 6(y^2) − 7x + 4y + 7 at the point (x,y)=(9,9)

the z(x,y) is throwing me off since it isnt f(x,y). Is there any difference?

I've done this problem about a million time, and am still not getting the right answer.

my solution:
\$\displaystyle z_x = 14x - 7 \$
\$\displaystyle z_x (9,9) = 14(9) - 9 = 119 \$

\$\displaystyle z_y = -12y + 4 \$
\$\displaystyle z_y = -12(9) + 4 = -104 \$

there is no value for z though which confuses me.

I know that an equation of the tangent plane to the surface z = f(x,y) at the point \$\displaystyle P (x_0, y_0, z_0) \$ is
\$\displaystyle z-z_0=f_x (x_0 ,y_0 )(x-x_0 ) + f_y (x_0, y_0)(y-y_0) \$

but when I plug in everything into this equation I get \$\displaystyle z = 119(x-9) - 104(y-9) \$ which is wrong. Any help would be appreciated.

\$\displaystyle z(9,9)\$ is the value of z.
• Jan 30th 2010, 05:30 PM
rain21
Quote:

Originally Posted by General
\$\displaystyle z(9,9)\$ is the value of z.

nvm solved it