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The line that passes through the points (0,1,1)(0,1,1) and (1,0,-1)(1,0,−1) has parametric equation given by
Find the points on the graph of the function f(x)=x+1/x-1. Where the slope of the tangent line is equal to -1/3 determine the equation of the tangent and normal to line

A conic section is given by the equation 57x^2+14√3 xy+43y^2-576=0, identity and sketch the conics.


A conic session is given by the equation 57x^2+14√3xy+43y^2-576=0
sketch and identify the curve defined by the parametric equations
(I). y=t+1 (II). x=t^2-2t (III). -4_< t _<6
Find the area of the region inside both the rose r =sin(2Φ) and the circle r=cosΦ.The appropriate graph and intervals to the best of your interest to solve this question 
The line x=y=z-1 intersects the cone x^2+y^2+z^2+2yz+2zx+2xy=0 at exactly one point
Verify that the point P(a cos θ, b sin θ) lies on the ellipse
x
2
a
2
+
y
2
b
2
= 1,
where a and b are the semi-major and semi-minor axes respectively of the ellipse . Find the
gradient of the tangent to the curve at P and show that the equation of the normal at P is
ax sin θ − by cos θ = (a
2 − b
2
) sin θ cos θ.
If P is not on the axes and if the normal at P passes through the point B(0, b), Show that
a
2 > 2b
2
. If further, the tangent at P meets the y-axis at Q, show that
|BQ| =
a
2
b
2
.
The xy-plane intersects the sphere x^2+y^2+z^2+2x+2y-z=2 in a great circle.
A statuary hall is elliptical in shape. It measures 42 feet wide and 96 feet long. If a person is standing at one focus, her whisper can be heard by a person standing at the other focus. How far apart are the two people
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