Analytic Geometry Answers

c) Find the angle between the x-axis and the tangent to the hyperbola xy = 9 at (3, 3).

Under what conditions on a, the sphere x^2+y^2+z^2+ax-y=0 and x^2+y^2+z^2+x+2z+1=0 intersect each other at an angle 45 degrees.

An elliptical riding path is to be built on a rectangular piece of property as shown below.
The rectangular piece of property measures 10 mi by 4 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides.

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Find the center, vertices, and foci of the ellipse with equation x squared divided by one hundred plus y squared divided by thirty six = 1



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Find an equation in standard form for the ellipse with the vertical major axis of length 18, and minor axis of length 16.

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Graph the ellipse with equation x squared divided by forty nine plus y squared divided by thirty six = 1

Let R be the point which divides the line segment joining P(2,1,0) and Q(-1,3,4) in the ratio 1:2 such that PR<PQ. Find the =n of the line passing through R and parallel to the line x/2=y/1=z/3

Find two unit vectors perpendicular to both A = ˆi − 2ˆj + 3kˆ
r
and B = −2ˆi + 4ˆj
r
.

Find the angel between the x-axis and the tangent to the hyperbola xy=9 at(3,3)

Find the path traced by the centre of the sphere which touches the lines
x/y = y/(-1) = z/2 and 2x = y , y-z = 0.