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

A circle touches the x-axis and also thouches the circle with center (0, 3) and radius 2. The locus of the center of the circle is (a)a circle (b) an ellipse (c)a parabola (d) a hyperbola

The locus of the point (sqrt(3h),(sqrt(3)k+2)) if it lies on the line x-y-1=0 is straight line (b) a circle 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 (a)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 equation (x^2)/(1-r)-(y^2)/(1+r)=1,r >1, represents (a)an ellipse (b) a hyperbola (c)a circle (d) none of these

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

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 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)

The curve described parametrically by x=t^2+t+1 , and y=t^2-t+1 represents. (a)a pair of straight lines (b) an ellipse (c)a parabola (d) a hyperbola

P(x , y) is a variable point on the parabola y^2=4a x and Q(x+c ,y+c) is another variable point, where c is a constant. The locus of the midpoint of P Q is an (a)parabola (b) ellipse (c)hyperbola (d) circle