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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
Analytic Geometry
Find the asymptotes of the hyperbola x2 −y2 + 2x + y + 9 = 0.
Analytic Geometry
Show that the points (2,0,1),(0,4,-3) and
(-2,5,0) are non-collinear.Hence find the equation of plane passing through them.
(-2,5,0) are non-collinear.Hence find the equation of plane passing through them.
Analytic Geometry
Two equal concurrent forces, each of F N have a resultant of 6 N. When the magnitude of one of the forces is doubled, the resultant becomes 11 N. Calculate the value of F and the angle between the forces.
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#340153 on Dec 2023
#340153 on Dec 2023