Question 32653
EQN.OF ELLIPSE IS ….(X+2)^2/9 +(Y-3)^2/4 = 1………….I						
STD.EQN.OF ELLIPSE  IS						
(X-H)^2/A^2 + (Y-K)^2/B^2=1…………………..II………….COMPARING WITH ABOVE EQN.I						
WHERE H,K IS CENTRE...SO H=-2 AND K=3 HENCE CENTRE IS (-2,3)..						
A^2=9….OR……A=-3…. AND…….A =+3						
B^2=4….OR……B=-2….AND….B=+2						
MINOR AXIS =2B=4…						
MAJOR AXIS =2A=6						
						
NOW TO PLOT THE ELLIPSE YOU NEED						
1.CENTRE COORDINATES…HERE THEY ARE (-2,3)						
2.LENGTHS OF AXES….HERE…..6 AND 4.						
3.EQNS.OF AXES…..MINOR AXIS IS…….X=H…OR…X=-2….OR…X+2=0						
MAJOR AXIS IS …….Y=K…..OR……Y=3….OR……..Y-3=0						
HAVING FOUND THE REQUIRED DATA,TAKE A SUITABLE SCALE…SAY 1 CM=1 UNIT OR SO AND PLOT						
1.MARK ORIGIN…O,X AXIS AND Y AXIS						
2.PLOT CENTRE (-2,3)…CALL IT C						
3.DRAW MAJOR AXIS Y-3=0…THIS IS A LINE THROUGH CENTRE PARALLEL TO X AXIS						
4.DRAW MINOR AXIS X+2=0….THIS IS A LINE THROUGH THE CENTRE PARALLEL TO Y AXIS.						
5.MARK MAJOR AXIS LENGTH OF 6 ALONG THE MAJOR AXIS PLOTTED ABOVE….TAKING 3 UNITS ON EITHER SIDE OF CENTRE.CALL IT AA'						
6.MARK MINOR AXIS LENGTH OF 4 ALONG THE MINOR AXIS PLOTTED ABOVE…TAKING 2 UNITS ON EITHER SIDE OF CENTRE.CALL IT BB'						
7.ELLIPSE PASSES THROUGH A,A',B AND B'.JOIN THEM SMOOTHLY BY A SMOOTH ELLIPTICAL CURVE.						
8.IF YOU NEED YOU CAN PLOT ADDITIONAL POINTS BY GIVING ARBITRARY VALUES FOR X AND FINDING CORRESPONDING VALUE OF Y						
						
THE SAME PROCEDURE YOU CAN REVERSE TO FIND THE EQN.OF AN ELLIPSE FROM THE GRAPH