For the ellipse `(x^(2))/(16)+(y^(2))/(9)=1` which of the following is true
A) Radius of auxiliary circle is 4 (B) Radius of director circle is 5
C) Length of major axis is 8 (D) Length of minor axis is 6

An ellipse sliding along coordinate axes.If the foci of ellipse are (1,1) and (3,3) .Then which of the following is/are correct? Radius of director circle of ellipse is 2sqrt(2) Length of major axis of ellipse is 2sqrt(5) Length of minor axis of ellipse is sqrt(3) Length of major axis of ellipse is

The ellipse (x^(2))/(25)+(y^(2))/(16)=1 with the major and minor axis in M and m respectively is

If the equation of an ellipse is 2x^2 + 3y^2 - 8x + 6y+5=0 , then which of the following is/are true? (A) equation of auxiliary circle is x^2 + y^2 - 4x + 2y + 2 = 0 (B) equation of director circle is x^2 + y^2 + 2y=0 (C) the director circle will pass through (4, -2) (D) none of these

If the foci of an ellipse (x^(2))/(9)+(y^(2))/(16)=1 are ends of diameter of a circle then finds the radius of the circle

Ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a>b) Equation of the circle described on major axis as diameter is

In an ellipse length of minor axis is 8 and eccentricity is (sqrt(5))/(3) . The length of major axis is

A point on the ellipse x^(2)/16 + y^(2)/9 = 1 at a distance equal to the mean of lengths of the semi - major and semi-minor axis from the centre, is

A circle intersects an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 precisely at three points A,B,C as shown in the figure.AB is a diameter of the circle and isperpendicular to the major axis of the ellipse. If the eccentricity oflipse is (4)/(5), find the length of the diameter AB in terms of a.