A point `P(x , y)` moves in the xy-plane such that `x=acos^2theta` and `y=2asintheta,` where `theta` is a parameter. The locus of the point `P` is a/an (A) circle (B) ellipse (C) unbounded parabola (D) part of the parabola

The locus of the point whose co-ordinates are x = 3 cos theta + 2 , y = 3 sin theta - 4 , where theta is a parameter , is

x=a cos theta, y=a sin theta is a parametric form of : (A) Parabola (B) Hyperbola (C) Ellipse (D) Circle

The locus of lhe point of intersection of the lines x+4y=2a sin theta,x-y=a cos theta where theta is a variable parameter is

If the coordinates of a variable point be (cos theta + sin theta, sin theta - cos theta) , where theta is the parameter, then the locus of P is

If a+b+3c=0, c != 0 and p and q be the number of real roots of the equation ax^2 + bx + c = 0 belonging to the set (0, 1) and not belonging to set (0, 1) respectively, then locus of the point of intersection of lines x cos theta + y sin theta = p and x sin theta - y cos theta = q , where theta is a parameter is : (A) a circle of radius sqrt(2) (B) a straight line (C) a parabola (D) a circle of radius 2

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

The Locus of the point (tan theta+sin theta,tan theta-sin theta) is (theta is a parameter) (x^(2)-y^(2))= kxy then (k)/(2)

If the co-ordinates of a point P are x = at^(2) , y = a sqrt(1 - t^(4)) , where t is a parameter , then the locus of P is a/an

The locus of the mid point of the focal radi of a variable point moving on the parabola,y^(2)=8x is a parabola whose-