Homework Sourseconsider a surface S whose equation is 4x29y28z2144 find the
consider a surface S whose equation is 4x^2+9y^2+8z^2=144. find the gradient and the equation of the tangent plane to the surface at the point A(3,-2,-3)
Solution
grad(f) = (8x , 18y , 16z) = (24 , -36 , -48)
So the tangent plane equation is:
24(x-3)-36(y+2)-48(z+3) = 0
2(x-3)-3(y+2)-4(z+3) = 0
so the equation is:
2x-3y-4z = 24
