Identify the intersection of the quadratic surface x24 y29

Identify the intersection of the quadratic surface x^2/4 - y^2/9 + z^2/25 - x + y + xy = 4 with the plane x = 5

Solution

If we visualize the two surfaces then we find that x=5 is a vertical plane at x=5 .

The quadratic surface in question will be another curve in plane x=5.

Now The interesction between the two will have to be an ellipse in the y-z plane .

At the point of intersection of the plane (x=5) and the elliptoid the value will be x =5

thus keeping x=5 in equation of elliptiod we get

25/4-y²/9+z²/25-5+y+5y=4

solving it we get

(y/3-3)²-(z/5)²=(5/2)^{2 Answer}