`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`

For the variable t, the locus of the points of intersection of lines x-2y=t and x+2y=(1)/(t) is

If points A and B are (1, 0) and (0, 1), respectively, and point C is on the circle x^2+y^2=1 , then the locus of the orthocentre of triangle A B C is (a) x^2+y^2=4 (b) x^2+y^2-x-y=0 (c) x^2+y^2-2x-2y+1=0 (d) x^2+y^2+2x-2y+1=0

For the variable t , the locus of the points of intersection of lines x - 2y = t and x + 2y = (1)/(t) is _

The orthocentre of the triangle formed by the lines x+y=1,2x+3y=6 and 4x-y+4=0 lies in

Orthocentre of the triangle formed by the lines x+y=1, x=0 and y=0 is-

Find the coordinates of the centroid of the triangle, formed by the lines x+2y-5=0, y+2x-7=0 and x-y+1=0 .

If tangents O Q and O R are dawn to variable circles having radius r and the center lying on the rectangular hyperbola x y=1 , then the locus of the circumcenter of triangle O Q R is (O being the origin). (a) x y=4 (b) x y=1/4 x y=1 (d) none of these

Tangent are drawn to the circle x^2+y^2=1 at the points where it is met by the circles x^2+y^2-(lambda+6)x+(8-2lambda)y-3=0,lambda being the variable. The locus of the point of intersection of these tangents is (a) 2x-y+10=0 (b) 2x+y-10=0 (c) x-2y+10=0 (d) 2x+y-10=0

P(x , y) is a variable point on the parabola y^2=4a x and Q(x+c ,y+c) is another variable point, where c is a constant. The locus of the midpoint of P Q is

In a triangle A B C , the bisectors of angles Ba n dC lies along the lines x=y a n d y=0. If A is (1,2) , then the equation of line B C is