From the point `A(6, -8)`, all possible lines are drawn to cut the x-axis. Find the locus of their middle points.

A straight line is drawn through the point P(2;3) and is inclined at an angle of 30^@ with the x-axis . Find the coordinates of two points on it at a distance 4 from point P.

The tangent at any point P on the circle x^2 + y^2 = 2 cuts the axes in L and M . Find the locus of the middle point of LM .

Three mutually perpendicular lines are drawn from the point (1,2,-1) . If one of the lines is perpendicular to the x-axis and the direction ratios of the second line are (1,2,-1) then which are the possible equation(s) of the third line

If O be origin and A is a point on the locus y^2=8x .find the locus of the middle point of OA

The straight line x/a+y/b=1 cuts the axes in A and B and a line perpendicular to AB cuts the axes in P and Q. Find the locus of the point of intersection of AQ and BP .

Through the point P(3,4) a pair of perpendicular lines are drawn which meet x-axis at the point A and B. The locus of incentre of triangle PAB is (a) x^(2)-y^(2)-6x-8y+25=0 (b) x^(2)+y^(2)-6x-8y+25=0 (c) x^(2)-y^(2)+6x+8y+25=0 (d) x^(2)+y^(2)+6x+8y+25=0

A stick of length l slides with its ends on two mutually perpendicular lines. Find the locus of the middle point of the stick.

Tangents are drawn to a unit circle with centre at the origin from each point on the line 2x + y = 4 . Then the equation to the locus of the middle point of the chord of contact is

OA and OB are two perpendicular straight lines. A straight line AB is drawn in such a manner that OA+OB=8 . Find the locus of the mid point of AB.

Through the vertex 'O' of parabola y^2=4x , chords OP and OQ are drawn at right angles to one another. Show that for all positions of P, PQ cuts the axis of the parabola at a fixed point. Also find the locus of the middle point of PQ.