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(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.

asked Apr 20, 2020 by balaji.thirumalai
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