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Geometry
2. 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 thegradient 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 thegradient 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 .
Geometry
1. (a) If a chord of the parabola y^2 = 4ax is a normal at one of its ends, show that its mid-point lies on the curve 2(x − 2a) = y^2/a + 8a^3/y^2
.
Prove that the shortest length of such a chord is 6a√3.
(b) Find the asymptotes of the hyperbola
x^2 − y^2 + 2x + y + 9 = 0.
.
Prove that the shortest length of such a chord is 6a√3.
(b) Find the asymptotes of the hyperbola
x^2 − y^2 + 2x + y + 9 = 0.
Geometry
Line PR is perpendicular to line QS, angle QPR=60°, angle PSR=30° and line PQ=8cm. Calculate line SR correct to two significant figures
Geometry
A learner in your class is confused about the concepts of perimeter and area. Use
examples to explain and illustrate the difference between these concepts.
examples to explain and illustrate the difference between these concepts.
Geometry
Mpho has a circular swimming pool with a radius of 6.2 m. She wants to buy net to
cover the pool completely. What is the minimum length and width of the piece of net
that she must buy to cover the pool?
cover the pool completely. What is the minimum length and width of the piece of net
that she must buy to cover the pool?
Geometry
Discuss how you will teach a Grade 9 class how to construct angle 45° without using
a protractor. In your discussion, include the steps that you will follow and all
mathematical instruments that you will use.
a protractor. In your discussion, include the steps that you will follow and all
mathematical instruments that you will use.
Geometry
Give one worked out example of an activity that you will do in class with your Grade
8 learners to develop their understanding of the volume of a cylinder (include drawings
that you will use).
8 learners to develop their understanding of the volume of a cylinder (include drawings
that you will use).
Geometry
1.The. interior angle of a regular polygon is five times it's corresponding exterior angle. Find the number of sides of the polygon.
2. A ladder 8.5m long leans against a vertical wall .the top (T) of the ladder makes angle of 58 degrees with the wall.how far, correct to one decimal place the foot of ladder from the wall
3./PR/ us perpendicular to /QR/.<QPR=60°.<PSR=30° and /PQ/=8cm calculate/PSR/, correct to two significant figures
4.Construct parallel line through a point by
I.by angles method
Ii.by rhombus method
2. A ladder 8.5m long leans against a vertical wall .the top (T) of the ladder makes angle of 58 degrees with the wall.how far, correct to one decimal place the foot of ladder from the wall
3./PR/ us perpendicular to /QR/.<QPR=60°.<PSR=30° and /PQ/=8cm calculate/PSR/, correct to two significant figures
4.Construct parallel line through a point by
I.by angles method
Ii.by rhombus method
Geometry
Line PR is perpendicular to line QS, angle QPR=60°, angle PSR=30° and line PQ=8cm. Calculate line SR correct to two significant figures
Geometry
Joe has 650 cm^2 of tin. He wants me to make a tin of can that can hold as much juice as possible. What dimensions should he use? What is the largest volume this can could have?
