1.consider the ellipse 4(x+y-5)^2+9(x-y+9)^2=36 then which of the following about its focci are correct:
a.both of them lie in third quadrant
b.both of them are in second quadrant
c.one lies in third quadrant and another in first
d.one lise in second and another in first
2.an ellipse of major axis 20 root 3 and mnor axis 20 slides along the co ordinate axes always remains confined in first quadrant .locus of centre of ellipse therefore describes the arc of a circle .the length of the arc is :
a.5 pi b.20pi c.5pi/3d. 20 pi/3
1.(x+y-5)=0 and x-y+9=0 are perpendicular to each other.
put X=x+y-5/sqrt(2) Y=x-y+9/sqrt(2)
thus ur equation now is :
4X2 + 9Y2=9
a2=9/4 b2=1 e=sqrt(5)/3
centre =(0,0) focus =(-+sqrt(5)/4,0)
in original centre would be (-2,7)
and for focus
thus x=+-sqrt(5)-16/8 both are negative corresponding y value is positive .
thus b is the answer.
hey buddy I m really tired so if I have done some calculation mistake kindly correct me.
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