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Find the equation of the hyperboloid shown in Figure 16$(\mathrm{A})$

$\left(\frac{x}{4}\right)^{2}+\left(\frac{y}{6}\right)^{2}=1+\left(\frac{z}{\sqrt{27}}\right)^{2}$

Calculus 3

Chapter 12

VECTOR GEOMETRY

Section 6

A Survey of Quadric Surfaces

Vectors

Vector Calculus

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in this question would have gone about the question on the hip. A polite, uh uh, that has one sheet. Then it has a formula X over a squared. Plus, why are over p square? It could use the oversee. Square plus one in discussion here were given the figure, and we try to look at on the X Y plan way. Have the X intercept in continuing the farm. And why intercept equal to the six this'll? One replies that that I must go to the far, and, uh, we must go to the six. Now to find the see here in this question What we look at the, uh, plan Z e go to nine. We have the thanks. We go to the eat and why you go to the trail. Yeah, and they would trade your bullet on. We should get. Always see, this will be the idea. And, uh, end up being could drill. So we should get now will be the X over eight. So from here we see done. So let me try to drive this now. Again. Yeah. So, um, with the n b, we can have the X over I square blood it's of a fall square and then plus why Over six square echo to dizzy over C squared plus one. Now we need to find a say in this question here to find the say industry question, we can try one value on the, uh, on the graph. We see that this one point here, that will be the X equal to, uh, eight and why you were equal to the zero and is the equal tonight. So that's gonna be the point on the girl fear and therefore we can looking at them Ganda 8/4 square. Plus, there are over six square ego to the night oversee square ankle plus one. And from here, we don't have the two square will be fall here. You going to 81 hour three squared plus one arginine less than 81. Office is square. If we go to the three, this implies that the C squared equals eighty one hundred three. So again, a C squared equal to the 27 and then we should be able to write this question now will be on the farm X over 16 on, then plus why square over 36 he could achieve the the square over 27 plus one on this will be the answer

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