A straight line moves such that the algebraic sum of the perpendiculars drawn to it from two fixed points is equal to `2k` . Then, then straight line always touches a fixed circle of radius. (a)`2k` (b) `k/2` (c) `k` (d) none of these

A straight line passes through a fixed point (6,8) : Find the locus of the foot of the perpendicular drawn to it from the origin O.

A straight line passes through a fixed point (6, 8). Find the locus of the foot of the perpendicular on it drawn from the origin is.

A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2,0), (0,2) and (1,1) on the line is zero. Find the coordinate of the point P.

A straight line moves so that the product of the length of the perpendiculars on it from two fixed points is constant. Prove that the locus of the feet of the perpendiculars from each of these points upon the straight line is a unique circle.

If the algebraic sum of the distances from the points (2,0), (0, 2) and (1, 1) to a variable line be zero then the line passes through the fixed point.

Prove that the locus of a point, which moves so that its distance from a fixed line is equal to the length of the tangent drawn from it to a given circle, is a parabola.

If the algebraic sum of the distances of a variable line from the points (2,0),(0,2), and (-2,-2) is zero, then the line passes through the fixed point. (a) (-1,-1) (b) (0,0) (c) (1,1) (d) (2,2)

A point moves such that the sum of the square of its distances from two fixed straight lines intersecting at angle 2alpha is a constant. Prove that the locus of points is an ellipse

The locus of a point which moves such that the sum of the square of its distance from three vertices of a triangle is constant is a/an (a)circle (b) straight line (c) ellipse (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