A straight line is drawn through `P(3,4)` to meet the axis of `x` and `y` at `Aa n dB` , respectively. If the rectangle `O A C B` is completed, then find the locus of `Cdot`

Tangent and normal drawn to a parabola at A(a t^2,2a t),t!=0 meet the x-axis at point B and D , respectively. If the rectangle A B C D is completed, then the locus of C is

A tangent is drawn to the parabola y^2=4a x at P such that it cuts the y-axis at Qdot A line perpendicular to this tangents is drawn through Q which cuts the axis of the parabola at R . If the rectangle P Q R S is completed, then find the locus of Sdot .

If a tangent to the parabola y^2=4a x meets the x-axis at T and intersects the tangents at vertex A at P , and rectangle T A P Q is completed, then find the locus of point Qdot

The straight line through a fixed point (2,3) intersects the coordinate axes at distinct point P and Q. If O is the origin and the rectangle OPRQ is completed then the locus of R is

A normal to the hyperbola, 4x^2_9y^2 = 36 meets the co-ordinate axes x and y at A and B. respectively. If the parallelogram OABP (O being the origin) is formed, then the locus of P is :-

A line passing through the point P(4,2) meets the x and y-axis at A and B respectively. If O is the origin, then locus of the centre of the circumcircle of triangle OAB is

Consider two lines L_1a n dL_2 given by a_1x+b_1y+c_1=0a n da_2x+b_2y+c_2=0 respectively where c1 and c2 !=0, intersecting at point PdotA line L_3 is drawn through the origin meeting the lines L_1a n dL_2 at Aa n dB , respectively, such that PA=P B . Similarly, one more line L_4 is drawn through the origin meeting the lines L_1a n dL_2 at A_1a n dB_2, respectively, such that P A_1=P B_1dot Obtain the combined equation of lines L_3a n dL_4dot

A variable line passes through a fixed point (x_(1),y_(1)) and meets the axes at A and B. If the rectangle OAPB be completed, the locus of P is, (O being the origin of the system of axes)

T P and T Q are tangents to the parabola y^2=4a x at Pa n dQ , respectively. If the chord P Q passes through the fixed point (-a ,b), then find the locus of Tdot

A straight line passing through P(3,1) meets the coordinate axes at Aa n dB . It is given that the distance of this straight line from the origin O is maximum. The area of triangle O A B is equal to