The vertices of the ellipse
`9x^(2)+4y^(2)-18x-27 =0` are

Options

A. `(1,+-2)`
B. `(1,+-3)`
C. `(1,+- 4)`
D. none of these

Answer

B

Explanation

the equation of the ellipse can be written as
`9(x^(2)-2x+1)+4y^(2)=36`
`implies 9(x-1)^(2)+4(y-0)^(2)=36implies ((x-1)^(2))/(2^(2))+((y-0)^(2))/(3^(2))=1`
shifiting the origin at(1,0) keeping the axes parallel to the coordinate axes , we have
`x=X+1,y+0`
the equation of the ellipse with reference to new origin is
`(X^(2))/(2^(2))+(Y^(2))/(3^(2))=1`
the coordinates these in (i) we reference to new orgin are
`(X=0,Y=+-3)`
substituting these in (i) we obtain `(1,+-3)` as the coordinates of the vertices of the given conic.