`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

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

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

o is the origin. A and B are variable points on y =x and x +y=0 such that the area of triangle OAB is k^2. The locus of the circumcentre of triangle OAB is

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at Aa n dB , respectively. A variable line perpendicular to L_1 intersects the x- and the y-axis at P and Q , respectively. Then the locus of the circumcenter of triangle A B Q is (a)3x-4y+2=0 (b)4x+3y+7=0 (c)6x-8y+7=0 (d) none of these

A=(1,2),B(3,4) and the locus of C is 2x+3y=5 then the locus of the centroid of Delta ABC is

The vertices A,B and C of a variable right triangle lie on a parabola y^(2)=4x. If the vertex B containing the right angle always remains at the point (1,2), then find the locus of the centroid of triangle ABC.

The vertices A,B and C of a variable right- angled triangle lie on a parabola y^(2)=4x .if the vertex B containing the right angle always remains at the point (1,2), then find the locus of the centroid of triangle ABC.

Parabola y^(2)=4a(x-c_(1)) and x^(2)=4a(y-c_(2)), where c_(1) and c_(2) are variable,are such that they touch each other. The locus of their point of contact is xy=2a^(2) (b) xy=4a^(2)xy=a^(2)(d) none of these

If vertices of a triangle ABC are A(1,2),B(3,4) and C(-5,3) and its orthocentre is O, then reflecton of orthocentre of triangle OBC w.r.t.line y=x will be (a,b) then a+b is equal to

The equation of the altitudes AD,BE,CF of a triangle ABC are x+y=0,x-4y=0 and 2x-y=0 respectively.If.A =(t,-t) where t varies,then the locus of centroid of triangle ABC is (A) y=-5x(B)y=x(C)x=-5y(D)x=y