`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`

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

The general solution of the differential equation y dx+(x+2y^2)dy=0 is a) x y+y^2=c b) 3x y+y^2=c c) x y+2y^3=c d) 3x y+2y^3=c

x=2, y=−1 is a solution of the linear equation (a) x+2y=0 (b) x+2y=4 (c) 2x+y=0 (d) 2x+y=5

Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid points of the chords of the circle C that subtend an angle of (2pi)/3 at its center is (a) x^2+y^2=3/2 (b) x^2+y^2=1 (c) x^2+y^2=27/4 (d) x^2+y^2=9/4

Equation of the parabola with focus (0,-3) and the directrix y=3 is: (a) x^(2)=-12y (b) x^(2)=12y (c) x^(2)=3y (d) x^(2)=-3y

(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

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

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

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

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