`(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

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

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

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

Area of the triangle formed by the lines y^2-9x y+18 x^2=0a n dy=6 is____

Find the vertices of the hyperbola 9x^2-16 y^2-36 x+96 y-252=0

Find the equation to the ausiliary circle of the ellipse 4x^(2) +9y^(2) -24x - 36 y + 36 = 0 .

The equation x^(2)y^(2)-9y^(2)-6x^(2)y+54y=0 represents

The equation of the circle passing through the point of intersection of the circle x^2+y^2=4 and the line 2x+y=1 and having minimum possible radius is (a) 5x^2+5y^2+18 x+6y-5=0 (b) 5x^2+5y^2+9x+8y-15=0 (c) 5x^2+5y^2+4x+9y-5=0 (c) 5x^2+5y^2-4x-2y-18=0

The orthocentre of the triangle formed by the lines 2x^(2)+3xy-2y^(2)-9x+7y-5=0 with 4x+5y-3=0 is