Equation auxiliary circle of the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`(a

Statement-1: Tangents drawn from any point on the circle x^(2)+y^(2)=225 to the ellipse (x^(2))/(144)+(y^(2))/(81)=1 are at a right angle. Statement -2 : Equation of the auxiliary circle of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 " is " x^(2)+y^(2)=a^(2) .

If PQR is an equilateral triangle inscribed in the auxiliary circle of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a>b) and P'Q'R' is corresponding triangle inscribed with the ellipse then centroid of the triangle P'Q'R' lies at

If the area of the auxiliary circle of the ellipse (x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1 (a gt b) is twice the area of the ellipse, then the eccentricity of the ellipse is

The intercept made by the auxiliary circle of the ellipse (x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1 (a gt b gt 1) on any tangent to the ellipse, subtends a right angle at its ceotre if

The area of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

Equation of director circle of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

Equations of the directrices of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a>b) are

The equation of the auxiliary circle of the ellipse (x^(2))/(12)+(y^(2))/(18)=1 is

The equation of the auxiliary circle of the ellipse (x^(2))/(12)+(y^2)/(18)=1 is