With a given point and line as focus and directrix, a series of ellipses are described. The locus of the extremities of their minor axis is an (a)ellipse (b)a parabola (c)a hyperbola (d)none of these

Find the locus of the middle points of chords of an ellipse drawn through the positive extremity of the minor axis

The locus of the point (sqrt(3h),sqrt(3k+2)) if it lies on the line x-y-1=0 is (a) straight line (b) a circle (c) a parabola (d) none of these

A line of fixed length a+b moves so that its ends are always on two fixed perpendicular straight lines. Then the locus of the point which divides this line into portions of length aa n db is (a) an ellipse (b) parabola (c) straight line (d) none of these

The curve in the first quadrant for which the normal at any point (x , y) and the line joining the origin to that point form an isosceles triangle with the x-axis as base is (a) an ellipse (b) a rectangular hyperbola (c) a circle (d) None of these

The locus of the midpoints of the chords of an ellipse x^(2) + 4y^(2) = 4 that are drawn forms the positive end of the minor axis is

Let S and S' be the foci of the ellipse and B be any one of the extremities of its minor axis. If DeltaS'BS=8sq. units, then the length of a latus rectum of the ellipse is

Show that the double ordinate of the auxiliary circle of an ellipse passing through the focus is equal to the minor axis of the ellipse .

Let the distance between a focus and the corresponding directrix of an ellipse be 8 and the eccentricity be 1/2 . If the length of the minor axis is k , then (sqrt(3)k)/2 is ____________

If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)/(16)=1 . Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse and if the product of eccentricities of hyperbola and ellipse is 1 then the equation of a. hyperbola is (x^2)/9-(y^2)/(16)=1 b. the equation of hyperbola is (x^2)/9-(y^2)/(25)=1 c. focus of hyperbola is (5, 0) d. focus of hyperbola is (5sqrt(3),0)

Find the locus of the midpoints of the all chords drawn from the ends points of the minor axis of an ellipse x^2/a^2+y^2/b^2=1