Analytic Geometry

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

Analytic Geometry

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

Analytic Geometry

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

Analytic Geometry

A conic session is given by the equation 57x^2+14√3xy+43y^2-576=0

Analytic Geometry

sketch and identify the curve defined by the parametric equations

(I). y=t+1 (II). x=t^2-2t (III). -4_< t _<6

(I). y=t+1 (II). x=t^2-2t (III). -4_< t _<6

Analytic Geometry

`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 `

Analytic Geometry

The line x=y=z-1 intersects the cone x^2+y^2+z^2+2yz+2zx+2xy=0 at exactly one point

Analytic Geometry

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

.

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

.

Analytic Geometry

The xy-plane intersects the sphere x^2+y^2+z^2+2x+2y-z=2 in a great circle.

Analytic Geometry

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