An ellipse is sliding along the coordinate axes. If the foci of the ellipse are (1, 1) and (3, 3), then the area of the director circle of the ellipse (in square units) is `2pi` (b) `4pi` (c) `6pi` (d) `8pi`

An ellipse passes through the point (2,3) and its axes along the coordinate axes, 3x +2y -1 = 0 is a tangent to the ellipse, then the equation of the ellipse is

The ratio of the perimeter (circumference) and diameter of a circle is (a) pi\ (b) 2pi (c) pi/2 (d) pi/4

A circle is inscribed in a square of side 14 m. The ratio of the area of the circle and that of the square is (a) pi:3\ (b) pi:4 (c) pi:2 (d) pi:1

The eccentricity of an ellipse with centre at the orgin and axes along the coordinate axes , is 1/2 if one of the directrices is x=4, the equation of the ellipse is

If the foci of an ellipse are (0,+-1) and the minor axis is of unit length, then find the equation of the ellipse. The axes of ellipse are the coordinate axes.

If the area of the ellipse ((x^2)/(a^2))+((y^2)/(b^2))=1 is 4pi , then find the maximum area of rectangle inscribed in the ellipse.

If the area of the ellipse ((x^2)/(a^2))+((y^2)/(b^2))=1 is 4pi , then find the maximum area of rectangle inscribed in the ellipse.

An ellipse intersects the hyperbola 2x^2-2y^2 =1 orthogonally. The eccentricity of the ellipse is reciprocal to that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then (a) the foci of ellipse are (+-1, 0) (b) equation of ellipse is x^2+ 2y^2 =2 (c) the foci of ellipse are (+-sqrt 2, 0) (d) equation of ellipse is (x^2 +y^2 =4)

The rate of change of the area of a circle with respect to its radius r at r = 6 cm is (A) 10pi (B) 12pi (C) 8pi (D) 11pi

The distance of a point on the ellipse (x^2)/6+(y^2)/2=1 from the center is 2. Then the eccentric angle of the point is pi/4 (b) (3pi)/4 (c) (5pi)/6 (d) pi/6