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Find the equation of a line that passes through the point (2,1) and has a gradient of
−
1
3
.
Leave your answer in the form
y
=
m
x
+
c
Plot the following points:
P1 (-3, 135°)
P2 (2, )
P3 (4, 405°)
Graph
Sketch the graph of r = 3 − 2cosθ.
Find the radius and centre of the circular section of sphere |r|= 4, cut off by the plane
r.(2i-j+4k)= 3.
- Convert the polar coordinates (-8, 2π/3) into rectangular coordinates.
- Convert the rectangular coordinates (3, -3) into polar coordinates with r > 0 and 0 ≤ θ < 2π.
- Convert the rectangular equation x2 + y2 = 100 into a polar equation that expresses r in terms of θ.
- Convert the polar equation 4r cos θ + r sin θ = 8 into a rectangular equation that expresses y in terms of x.
Exercise 6.1
Plot the following points:
1.P1 (-3, 135°)
P2 (2, -3.14/3)
P3 (4, 405°)
Then graph
2.Sketch the graph of r = 3 − 2cosθ.
Find the equations of the tangent and normal to each of the following conics, the lengths of the subtangent and subnormal, then trace the curve showing these lines.
y = x2 – 6x + 4 at (4, -4).
1.Convert the polar coordinates (-8, ) into rectangular coordinates.
2.Convert the rectangular coordinates (3, -3) into polar coordinates with r > 0 and 0 ≤ θ < 2π.
3.Convert the rectangular equation x2 + y2 = 100 into a polar equation that expresses r in terms of θ.
4.Convert the polar equation 4r cos θ + r sin θ = 8 into a rectangular equation that expresses y in terms of x.
Plot the following points:
P1 (-3, 135°)
P2 (2, )
P3 (4, 405°)
Graph
Sketch the graph of r = 3 − 2cosθ.
Find the equations of the tangents and normal to the following curves:
1. y2 + 8x = 0, parallel to x + y + 4 = 0.
2. x2 = 3y, perpendicular to x – 2y + 7 = 0.
3. x2 + 9y2 = 25, parallel to 4x + 9y + 30 = 0.
4. 25x2 + 4y2 = 100, perpendicular to 8x – 15y + 4 = 0.
5. x2 – y2 = 15, parallel to 4x – y + 20 = 0.
Find the equation of the circle(x - 5)2 + (y + 3)2 = 25 translated through a vector
(-2,-2). Also Sketch it.
