`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

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

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 DeltaA B C is (a) x+y=0 (b) x-y=0 x^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

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at A and B , 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

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

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

Parabola y^2=4a(x-c_1) and x^2=4a(y-c_2) where c_1 and c_2 are variables, touch each other. Locus of their point of contact is

The locus of the centre of the circle touching the line 2x-y=1 at (1, 1) and also touching the line x+2y =1 is : (A) x+3y = 2 (B) x+2y=3 (C) x+y=2 (D) none of these

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 (a) parabola (b) hyperbola (c) circle (d) none of these

The area of the triangle formed by the line x=3,\ \ y=4 and x=y is (a) 1/2 sq. unit \ (b) 1 sq. unit (c) 2 sq. unit (d) None of these