Line `x/a+y/b=1` cuts the co-ordinate axes at A(a,0) and B(0,b) and the line `x/a'+y/b'=-1` at `A'(-a',0)` and `B'(0,-b')`. If the points A,B,A',B' are concyclic then the orthocentre of triangle ABA' is

Show that the points (a,0),(0,b) and (x,y) are collinear if x/a+y/b=1.

The incentre of the triangle formed by axes and the line x/a+y/b=1 is

The straight line x/a+y/b=1 cuts the coordinate axes at A and B . Find the equation of the circle passing through O(0,0),Aa n dBdot

A line meets the co-ordinates axes at A(a, 0) and B(0, b) A circle is circumscribed about the triangle OAB. If the distance of the points A and B from the tangent at origin to the circle are 3 and 4 repectively, then the value of a^(2) + b^(2) + 1 is

The plane x/a+y/b+z/c=1 meets the co-ordinate axes in the point A, B, C respectively. Find the area triangle ABC.

The algebraic sum of distances of the line ax + by + 2 = 0 from (1,2), (2,1) and (3,5) is zero and the lines bx - ay + 4 = 0 and 3x + 4y + 5=0 cut the coordinate axes at concyclic points. Then (a) a+b=-2/7 (b) area of triangle formed by the line ax+by+2=0 with coordinate axes is 14/5 (c) line ax+by+3=0 always passes through the point (-1,1) (d) max {a,b}=5/7

A B C is a variable triangle such that A is (1, 2), and Ba n dC on the line y=x+lambda(lambda is a variable). Then the locus of the orthocentre of "triangle"A B C is x+y=0 (b) x-y=0 x^2+y^2=4 (d) x+y=3

A B C is a variable triangle such that A is (1,2) and B and C lie on line y=x+lambda (where lambda is a variable). Then the locus of the orthocentre of triangle A B C is (a) (x-1)^2+y^2=4 (b) x+y=3 (c) 2x-y=0 (d) none of these

If P(x , y) is any point on the line joining the point A(a ,0)a n dB(0, b), then show that x/a+y/b=1.

The line x/6+y/8=1 cuts the co-ordinate axis at A\ &\ B . If O is origin, then prodsinA/2 for the triangle O A B is 5/6 (b) 1/(10) (c) 5/4 (d) none of these