Q)
(chatquestion)...1. Plot the point in polar coordinates and find the corresponding rectangular coordinates
for the point
(a) (4, 37/6), (b) (-1,57/4),
(c) (-4, -7/3),
(d) (0,-77/6)
2. Find two sets of polar coordinates for the following rectangular Cartesian coordinates
and plot them for 0<0 < 2n.
(a) (1, 1),
(b) (0, –5),
(c) (-3,4),
(d) (3, –1).
3. Find the Cartesian equations of the lines or curves whose polar equations are
(a) r = a
(b) r = acos 20
(c) r2 = a? sin 20
(d) r= a(1 + cos 20)
(e) r = a sec(0 - a)
4. Find the polar equations of the lines or curves whose Cartesian equations are
(a) (r - a)? + (y – a)? = a?
(b) x2/a? + y?/b2 = 1
(c) y = 2x
(d) y = x2
(e) xy = 4
(f) y = 4 (g) 3x – y +2 = 0.
5. * Find the points of horizontal and vertical tangency, if any, to the polar curve
r = 1+ sin 0.
6. Find the points of horizontal tangency, if any, to the polar curves r = 2cosece + 3
and r = 4 sin 0 cos? 0.
7. Trace the curves or lines whose polar equations are given below stating, where ap-
propriate, the equations of the tangents at the pole
(a) r = 3 sin 0
(b)* r = 2 cos 30
(c) r = 3 sin 20
(d)* r = 3 – 2 cos e
(e) r2 = 4 cos 20.
(f)* r = 3cosece
(g) r = 1- sin 0.
8. Sketch and identify the conics whose polar equations are
(a)* r = -1/(1 – sin 6)
(b)* r = 6/(2 + cos e)
(c) r(2+ sin 0) = 4
(d) r= 3/(2 + 6 sin 0)
9. Show that the polar equation for the ellipse r2/a²+y²/b2 = 1 is r2 = b/(1-e2 cos? 0).
10. * Find the area of the sector enclosed by the curve whose equation in polar coordinates
is r = a sec? 0/2 and the radii 0 = 0, 0 = a where a < T.
11. Sketch the curve r = a(1+ sin 0). Find the ratio of the area above
ne to
the total area bounded by the curve.
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