If the segment joining (a,b) and (c,d) subtends a right angle at the origin, show that ac+bd = 0.

If the segments joining the points A(a , b)a n d\ B(c , d) subtends an angle theta at the origin, prove that : theta=(a c+b d)/((a^2+b^2)(c^2+d^2))

The condition on a and b , such that the portion of the line a x+b y-1=0 intercepted between the lines a x+y=0 and x+b y=0 subtends a right angle at the origin, is a=b (b) a+b=0 a=2b (d) 2a=b

If the line x+2y+4=0 cutting the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 in points whose eccentric angies are 30^(@) and 60^(@) subtends right angle at the origin then its equation is

If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the segment, the four points are concyclic (i.e. lie on the same circle).

Show that all chords of the curve 3x^2 -y^2- 2x+ 4y= 0 , which subtend a right angle at the origin, pass through a fixed point. Find the co-ordinates of the point.

The locus of the midpoint of a chord of the circle x^2+y^2=4 which subtends a right angle at the origins is (a) x+y=2 (b) x^2+y^2=1 (c) x^2+y^2=2 (d) x+y=1

Let z_1 and z_2 be nth roots of unity, which subtend a right angle at the origin. Then n must be of the form:

Let S =x^2 + y^2 + 2gx + 2fy +c = 0 be a gives circle. Find the locus of the foot of the perpendicular drawn from the origin upon any chord, which subtends a right angle at the origin.

If C is a point on the line segment joining A (-3, 4) and B (2, 1) such that AC = 2BC, then the co-ordinates of C are :