Q.1 92.2 + 12y-108 (a) Show that the curve is a conic and state what type of con

Question

Q.1 92.2 + 12y-108 (a) Show that the curve is a conic and state what type of conic it is. (b) Write down:- (i) the coordinates of any vertices; (ii) the eccentricity of the conic (ii) the coordinates of any foci; (iv) the equations of any directrices. (c) Sketch the conic, marking on your sketch any vertices, foci and directrices from part (b), labelling them with their coordinates or equations as appropriate. Q.2 semicircle with endpoints (2, -2) and (2, 4) y (2,4) (a) Write the coordinates of the midpoint of the line segment and the radius of the semicircle. (b) Write down a parametrisation of the line segment. (c) Write down a parametrisation of the semicircle. In parts (b) and (c), specify the range of values for the parameter

Explanation / Answer

1. a. 9x2+12y2=108 X2/12+y2/9=1 Ellipse

b. i. (root2/3,0) vertices. ii. Eccentricity e=1/root12 iii.coordinates of focii =(root3,0) iv.equation of adirectrix x=2root3/(1/2rot3)=12

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