If `z=3/(2+costheta+"isin"theta)` then locus of `z` is a. straight line b. a circle having center on the y-axis c. a parabola d. a circle having center on the x-axis

The axis of the parabola y^2 = x is the line

If z^2+z|z|+|z^2|=0, then the locus z is a. a circle b. a straight line c. a pair of straight line d. none of these

Find the equation of the circle having center at (2,3) and which touches x+y=1

Prove that the locus of the center of the circle which touches the given circle externally and the given line is a parabola.

The locus of the center of a circle which cuts orthogonally the parabola y^2=4x at (1,2) is a curve

Find the locus of center of circle of radius 2 units, if intercept cut on the x-axis is twice of intercept cut on the y-axis by the circle.

The locus of the midpoint of a line segment that is drawn from a given external point P to a given circle with center O (where O is the orgin) and radius r is (a)a straight line perpendiculat to P O (b)a circle with center P and radius r (c)a circle with center P and radius 2r (d)a circle with center at the midpoint P O and radius r/2dot

If P= (1,0);Q=(-1,0) & R= (2,0) are three given points, then the locus of the points S satisfying the relation, SQ^2 + SR^2 =2SP^2 is - (a)a straight line parallel to x-axis (b) A circle through origin (c) A circle with center at the origin (d)a straight line parallel to y-axis

Prove that the locus of the center of a circle, which intercepts a chord of given length 2a on the axis of x and passes through a given point on the axis of y distant b from the origin, is a parabola.

P is the variable point on the circle with center at CdotC A and C B are perpendiculars from C on the x- and the y-axis, respectively. Show that the locus of the centroid of triangle P A B is a circle with center at the centroid of triangle C A B and radius equal to the one-third of the radius of the given circle.