Question

1 = (c). Consider the plane curve 1 5-5sin (i). Determine whether the curve is a circle, ellipse, parabola or hyperbola. Show the calculation of eccentricity and directrix of the curve. (15 marks) (ii). Convert the equation of the curve to the Cartesian form. (30 marks) copy the questions Answer all questions in separate papers. Take a clear picture of your solutions and them in the box below.

Answer 1

5 - 5sino on 1 5(1-sino) 1/5 = or ΟΥ. 5 (1-sino) ok (1-sino) 1- Cos (1/2-0) Comparing with the education the Conie = 1-ecoso We get; d = 1/5 and e = 1 and o'= (1 - 0) Since, e = 1; So; the Given Conie is Parabola. (Ang) We knoco that, the equation of directoix of :- 1 - coso is l f -Cosol So; Hore the equation of dineetrix is - . Cos o or 1/5 - cos (2-0) on 1/5 = - Sino on, & sino = 1/5 y = -1/5 on (An

= cl 1 5- 5 sino on, 57-58 sino=1. and Liet, x= = neoso y=nsino - ces 2 or plus) 1 ² = x² + y² 54 = 1 (1+54) 25 m2 = (1+546) on 25 (x² + y 2) = 1+ loy +2542 on 25x² = 1 +loy (104+1) on 25 2. on 25 x on. X 1 25 10.1y+ To dde 12 (y + 10). (AN) on