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 plane passes through a fixed point (a ,b ,c)dot Show that the locus of the foot of the perpendicular to it from the origin is the sphere x^2+y^2+z^2-a x-b y-c z=0.

Find the coordinates of the foot of the perpendicular P from the origin to the plane 2x-3y+4z-6=0

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.

Consider the straight line 3x + 4y + 8 = 0  i. What is the slope of the line which is perpendicular to the given line? ii. If the perpendicular line passes through (2,3), form its equation,  iii. Find the foot of the perpendicular drawn from (2,3) to the given line.

Two straight lines pass through the fixed points (+-a, 0) and have slopes whose products is pgt0 Show that the locus of the points of intersection of the lines is a hyperbola.

The ends A and B of a straight line segment of constant length c slide upon the fixed rectangular axes OX and OY, respectively. If the rectangle OAPB be completed, then the locus of the foot of the perpendicular drawn from P to AB is

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.

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

the locus of the foot of perpendicular drawn from the centre of the ellipse x^2+3y^2=6 on any point: