Question 36551
TIP:
IF X^2 AND Y^2 HAVE DIFFERENT COEFFICIENTS OF SAME SIGN ,THEN IT COULD
BE ELLIPSE.
4.) 4(x-1)2 = 4-y2
I HOPE IT IS
4(X-1)^2+Y^2=4...DIVIDE WITH 4
(X-1)^2/1^2+Y^2/2^2=1
THIS THE EQN.OF AN ELLIPSE.STD.EQN. IS
(X-H)^2/A^2 +(Y-K)^2/B^2=1
WHERE
(H,K) IS CENTRTE....(1,0).HERE
LENGTH OF MAJOR AXIS IS 2B...2*2=4
MINOR AXIS IS ALONG Y=K....Y=0
LENGTH OF MINOR AXIS IS 2A...2*1=2
ECCENTRICITY=E=SQRT{(B^2-A^2)/A^2}
=SQRT(4-1)/1=SQRT(3)
B*E=2SQRT(3)
B/E=2/SQRT(3)
FOCI ARE (H,K+BE) AND (H,K-BE)
(1,2SQRT(3)) AND (1,-2SQRT(3))
DIRECTRIX ARE.Y=K+B/E AND K-B/E
Y=2/SQRT(3)..AND...Y=-2/SQRT(3)
GRAPH IS GIVEN BELOW...
{{{ graph( 500, 500, -3, 3, -3, 3, (4-4*(x-1)^2)^0.5,-(4-4*(x-1)^2)^0.5) }}}
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