`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 (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

(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 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

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

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 variable chord of the circle x^2+y^2=4 is drawn from the point P(3,5) meeting the circle at the point A and Bdot A point Q is taken on the chord such that 2P Q=P A+P B . The locus of Q is (a) x^2+y^2+3x+4y=0 (b) x^2+y^2=36 (c) x^2+y^2=16 (d) x^2+y^2-3x-5y=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

Tangents P A and P B are drawn to x^2+y^2=9 from any arbitrary point P on the line x+y=25 . The locus of the midpoint of chord A B is (a) 25(x^2+y^2)=9(x+y) (b) 25(x^2+y^2)=3(x+y) (c) 5(x^2+y^2)=3(x+y) (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

If x=9 is the chord of contact of the hyperbola x^2-y^2=9 then the equation of the corresponding pair of tangents is (A) 9x^2-8y^2+18x-9=0 (B) 9x^2-8y^2-18x+9=0 (C) 9x^2-8y^2-18x-9=0 (D) 9x^2-8y^2+18x+9=0