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`

2x-y=4,x-2y+1=0

From the points (3, 4), chords are drawn to the circle x^2+y^2-4x=0 . The locus of the midpoints of the chords is (a) x^2+y^2-5x-4y+6=0 (b) x^2+y^2+5x-4y+6=0 (c) x^2+y^2-5x+4y+6=0 (d) x^2+y^2-5x-4y-6=0

Ba n dC are fixed points having coordinates (3, 0) and (-3,0), respectively. If the vertical angle B A C is 90^0 , then the locus of the centroid of A B C has equation. (a) x^2+y^2=1 (b) x^2+y^2=2 (c) 9(x^2+y^2)=1 (d) 9(x^2+y^2)=4

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

In triangle A B C , the equation of side B C is x-y=0. The circumcenter and orthocentre of triangle are (2, 3) and (5, 8), respectively. The equation of the circumcirle of the triangle is a) x^2+y^2-4x+6y-27=0 b) x^2+y^2-4x-6y-27=0 c) x^2+y^2+4x-6y-27=0 d) x^2+y^2+4x+6y-27=0

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=2 (c) x+y=2 (d) none of these

A triangle is formed by the lines x+y=0,x-y=0, and l x+m y=1. If la n dm vary subject to the condition l^2+m^2=1, then the locus of its circumcenter is (a) (x^2-y^2)^2=x^2+y^2 (b) (x^2+y^2)^2=(x^2-y^2) (c) (x^2+y^2)^2=4x^2y^2 (d) (x^2-y^2)^2=(x^2+y^2)^2

A tangent at a point on the circle x^2+y^2=a^2 intersects a concentric circle C at two points Pa n dQ . The tangents to the circle X at Pa n dQ meet at a point on the circle x^2+y^2=b^2dot Then the equation of the circle is (a) x^2+y^2=a b (b) x^2+y^2=(a-b)^2 (c) x^2+y^2=(a+b)^2 (d) x^2+y^2=a^2+b^2

(6,0),(0,6),a n d(7,7) are the vertices of a A B C . The incircle of the triangle has equation. (a) x^2+y^2-9x-9y+36=0 (b) x^2+y^2+9x-9y+36=0 (c) x^2+y^2+9x+9y-36=0 (d) x^2+y^2+18 x-18 y+36=0

The straight lines joining any point P on the parabola y^2=4a x to the vertex and perpendicular from the focus to the tangent at P intersect at Rdot Then the equation of the locus of R is (a) x^2+2y^2-a x=0 (b) 2x^2+y^2-2a x=0 (c) 2x^2+2y^2-a y=0 (d) 2x^2+y^2-2a y=0