If `(x_1, y_1)` be the centroid of the triangle formed by a line `L` and coordinate axes then equation of line `L` is a. `(3x)/(x_1)+(3y)/(y_1)=1` b. `xx_1+y y_1=3` c. `x/(3x_1)+y/(3y_1)=1` d. `x/(x_1)+y/(y_1)=1` e. `x x_1+y y_1=1`

The circumcentre of the triangle formed by the lines x+y-1=0,x-y-10,x-3y+3=0 is

The orthocenter of the triangle formed by the lines x+y+1=0, x-y-1=0, 3x+4y+5=0 is :

The distance of the line 2x-3y=4 from the point (1,1) in the direction of the line x+y=1 is

The centroid of the triangle formed by A(x_(1),y_(1)),B(x_(2),y_(2)),C(x_(3),y_(3)) is

In a triangle ABC ,the bisectors of angles BandC lies along the lines x=y and y=0 . If A is (1,2) ,then the equation of line BC is (a) 2x+y=1 (b) 3x-y=5 (c) x-2y=3 (d) x+3y=1

The equation of the circle circumscribing the triangle formed by the lines x=1,y=1,x+y=3 is

The equation to the chord joining two points (x_1,y_1) and (x_2,y_2) on the rectangular hyperbola xy=c^2 is: (A) x/(x_1+x_2)+y/(y_1+y_2)=1 (B) x/(x_1-x_2)+y/(y_1-y_2)=1 (C) x/(y_1+y_2)+y/(x_1+x_2)=1 (D) x/(y_1-y_2)+y/(x_1-x_2)=1

Theorem : The area of a triangle the coordinates of whose vertices are (x_1;y_1);(x_2;y_2)and (x_3;y_3) is 1/2|(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|

The equation of the straight line passing through the point (4,3) and making intercepts on the co-ordinate axes whose sum is -1 is (a) (x)/(2)-(y)/(3)=1 and (x)/(-2)+(y)/(1)=1(x)/(2)-(y)/(3)=-1 and (x)/(-2)+(y)/(1)=-1 (c) (x)/(2)+(y)/(3)=1 and (x)/(2)+(y)/(1)=-1(x)/(2)+(y)/(1)=-1 and (x)/(-2)+(y)/(1)=-1

If the tangent at (x_(1),y_(1)) to the curve x^(3)+y^(3)=a^(3) meets the curve again in (x_(2),y_(2)), then prove that (x_(2))/(x_(1))+(y2)/(y_(1))=-1