Question

(a) Given the equation of a coule section as: 

9x² + 25y₂ - 36x - 150y +36 = 0. 

(i) Express the equntion in standard form. 

(ii) Determine the center, foci, vertics and directrices of the comic and hence, sketch its graph slowing all the information.

(b) Let Q(0,3) and R(0,-3) 

(i) Determine the low of points P such that |QP|=2|RP| 

(ii) Shaw that the locus is a circle and find its center and radiis. 

(iii) Find the equation of the tangent to the circle at the point Q(0,3) 

(c) A far wishes to Inuild a three-sided fence next to a ledge row, which forms the fourth side of a rectangular region. If the area is to equal 1800-m³, find the dimensions of the fence which minimize the perimeter. [6, 9, 5]

Answer 1

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Pago No Dab 2 2-5 2 -23 * 9x² + 254²_364 - 150 150y +36=0 (32) 2-2x34x6 +90 2x syx/S +36=0 Adding 152 both leder (3x) - 2x3xx6+6² + sy² - 2xsy XI5 + 15² 15² a - 1714 2 251 = ($I - hs) + (9-xe) 1= (-B + -6713) 2 -43 2 52 32 2,3 Deckel foc e ² I- 62 - 1-3? aa 52 = 4/5 ano (2x ae, 3c D wing - ( 2+ sayo 3) F2= (2-a (13) (2-413) = (+213) Verten V= (2+5,3) = (1, 3) Shta, k) 12=42-5, 3} = (-313) (h-aik) Direction DPE 2 RPL let & be tegy cutanu Formula (-)-(4-3) > 269)+(4+3)2 Squaring both side x² + 9 + 9 -6y = 4 { x² + y 249 +by) 3x2+3y2 + 307 +27= 0 or x² + y²+loy+9=0 hence ite a curile - 5 h x = 2+ a Centre - 2+ 5 S2+25 h h b R = g ² + 2 c = 0+25-9 = + 2 * 33 Y

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