Geometry Central Conicoid (part 1) Equation of the Tangent Plane to the Central Conicoid

Problem 1 Find the equation of the tangent plane to the central conicoid x2 – 4y2 + 3z2 + 2 = 0 at the point (1,2,0). Problem 2 Find whether the plane 2x + 3y + 2z =3 touches the central conicoid 2x2 + 3y2 + z2 = 1 or not.

Solution for finding the tangent plane of an ellipsoid which pass through a given line.

Central Conicoids (Part II) Equation of the Tangent Plane to the Ellipsoid Find the equation of the tangent plane to the ellipsoid 7x2 + 5y2 + 3z2 = 60 which pass through the line 5y – 3z = 0 = 7x + 10y – 30.

I need to solve for s in the following equation

I need to solve for s. The difficulty here is I don't know how to show a 'divide' sign on my computer. I have to solve for s. s(tan47) = s(tan28) + 7s, with the portion on the right side of the equal sign divided by s. When solving for s, I did the following: 1. Dividing the right hand side of the equation by s, I get: s(tan47) = s(tan28) + 7 2. The next step is to move the s to one side of the equal sign: s(tan47) - s(tan28) = 7 This is the part where I cannot remember what to do next. Thanks

prove a theorem(segment addition)

In a metric geometry, if A-B-C, P-Q-R,AB~PQ,and BC~QR, then AC~PR.

a metric geometry proof

In the taxi-cab plane show that ifA=(-5/2,2),B=(1/2,2), C=(2,2), P=(0,0), Q=(2,1) and R=(3,3/2)then A-B-C and P-Q-R. Show that line segment AB~toline segment PQ,line segment BC~line segmentQR, line segment AC~line segment PR. Sketch an appropriate picture.