A varaibla point `P` on a given ellipse of eccentricity `e` is jointed to its foci `S` and `S\'`. Let `I` be the incentre of `DeltaPSS\'` and curve `C\' be the locus of `I`. Curve `C` is a conic which is : (A) a parabola (B) a hyperbola which is not a rectangular hyperbola (C) an ellipse (D) a rectangular hyperbola

A parabola is drawn to pass through A and B the ends of a diameter of a given circle of radius a and to have as directrix a tangent to a concentric circle of radius b , the axes being AB and a perpendicular diameter. The locus of the focus of the parabola is a conic which is : (A) a parabola (B) an ellipse (C) a hyperbola which is not a rectangular hyperbola (D) a rectangular hyperbola

A variable point P on the ellipse of eccentricity e is joined to the foci S and S' . The eccentricity of the locus of incentre of the triangle PSS' is (A) sqrt((2e)/(1+e)) (B) sqrt(e/(1+e)) (C) sqrt((1-e)/(1+e)) (D) e/(2(1+e))

The locus of the mid - points of the parallel chords with slope m of the rectangular hyperbola xy=c^(2) is

Locus of the centre of the circle touching circles |z|=3 and |z-4|=1 externally is (A) a parabola (B) a hyperbola (C) an ellipse (D) none of these

The curve for which the length of the normal is equal to the length of the radius vector is/are (a) circles (b) rectangular hyperbola (c) ellipses (d) straight lines

The curve for which the length of the normal is equal to the length of the radius vector is/are (a) circles (b) rectangular hyperbola (c) ellipses (d) straight lines

The number of normal (s) of a rectangular hyperbola which can touch its conjugate is equal to

The locus of the point (x ,y) which moves such that sin^(-1)2x+sin^(-1)y=pi/2 is a circle b. a hyperbola c. a straight d. an ellipse

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

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