The given inequality shows an ellipse with a center at (1,-2)
The major axis will be [tex]a=\sqrt{\dfrac{26}{9} }[/tex]
The minor axis will be [tex]b=\sqrt{\dfrac{26}{4} }[/tex]
The equation of an ellipse is written in the form
[tex]\dfrac{(x-h)^2}{a^2} +\dfrac{(y-k)^2}{b^2} =1[/tex]
The center is (h,k) and the larger of a and b is the major radius and the smaller is the minor radius.
Now the given inequality is
[tex]9x^2+18x+4y^2+16y-11 > 0[/tex]
[tex]9x^2+18x+4y^2+16y > 11[/tex]
[tex]9(x^2-2x)+4(y^2+4y) > 11[/tex]
[tex]9(x^2-2x+1)+4(y^2+4y+4) > 11+9+16[/tex]
[tex]9(x^2-2x+1)+4(y^2+4y+4) > 26[/tex]
On further solving
[tex]9(x-1)^2+4(y+2)^2 > 26[/tex]
[tex]\dfrac{(x-1)^2}{\dfrac{26}{9} } + \dfrac{(y+2)^2}{\dfrac{26}{4} } > 1[/tex]
Thus by comparing the equation with the standard form
[tex]\dfrac{(x-h)^2}{a^2} +\dfrac{(y-k)^2}{b^2} =1[/tex]
Thus we can see that the center (h,k) is (1,-2)
The major axis will be [tex]a=\sqrt{\dfrac{26}{9} }[/tex]
The minor axis will be[tex]a=\sqrt{\dfrac{26}{4} }[/tex]
To know more about ellipse follow
https://brainly.com/question/19507943
Answer:
ellipse with a dashed line boundary
(1,-2)
(-2,0)
Step-by-step explanation:
assignment
