Line `x/a+y/b=1` cuts the coordinate axes at `A(a ,0)a n dB(0,b)` and the line `x/a^(prime)+y/b^(prime)=-1` at `A (-a ,)` and `B^(prime)(0,-b^(prime))dot` If the points `A ,B ,A^(prime),B '` are concyclic, then the orthocentre of triangle `A B A '` is

Line x/a+y/b=1 cuts the coordinate axes at A(a,0) and B(0,0) 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 the triangle ABA' is

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

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),A and B.

Using determinants prove that the points (a ,\ b),\ (a^(prime),\ b^(prime))a n d\ (a-a^(prime),\ b-b^(prime)) are collinear if a b^(prime)=a^(prime)bdot

If a and b are co-primes , then their LCM is .

If the normal to the given hyperbola at the point (c t , c/t) meets the curve again at (c t^(prime), c/t^(prime)), then (A) t^3t^(prime)=1 (B) t^3t^(prime)=-1 (C) t t^(prime)=1 (D) t t^(prime)=-1

If Aprime=[-2 3 1 2] and B=[-1 0 1 2] , then find (A+2B)^(prime) .

The sum of the intercepts on the coordinate axes made by a line passing through the point (a, b) and the common point of (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 is

Two fixed points A and B are taken on the coordinates axes such that O A=a and O B=b . Two variable points A ' and B ' are taken on the same axes such that O A^(prime)+O B^(prime)=O A+O Bdot Find the locus of the point of intersection of A B^(prime) and A^(prime)Bdot

Show the condition that the curves a x^2+b y^2=1 and a^(prime)\ x^2+b^(prime)\ y^2=1 Should intersect orthogonally