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

Let a line L_(1):3x+2y-6=0 intersect the x and y axes at P and Q respectively.Let another line L_(2) perpendicular to L_(1) cut the x and y axes at R and S respectively.The locus of point of intersection of the lines PS and QR is

ABC 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 ABC is (a)(x-1)^(2)+y^(2)=4(b)x+y=3( c) 2x-y=0 (d) none of these

A line intersects x-axis at A(2, 0) and y-axis at B(0, 4) . A variable lines PQ which is perpendicular to AB intersects x-axis at P and y-axis at Q . AQ and BP intersect at R . Image of the locus of R in the line y = - x is : (A) x^2 + y^2 - 2x + 4y = 0 (B) x^2 + y^2 + 2x + 4y = 0 (C) x^2 + y^2 - 4y = 0 (D) x^2 + y^2 + 2x - 4y = 0

From a point P=(3,4) perpendiculars PQ and PR are drawn to line 3x+4y-7=0 and a variable line y-1=m(x-7) respectively then maximum area of triangle PQR is :

The line 2x+3y=6, 2x+3y-8 cut the X-axis at A,B respectively. A line L=0 drawn through the point (2,2) meets the X-axis at C in such a way that abscissa of A,B,C are in arithmetic Progression. then the equation of the line L is

A line intersects x-axis at A(2, 0) and y-axis at B(0, 4) . A variable lines PQ which is perpendicular to AB intersects x-axis at P and y-axis at Q . AQ and BP intersect at R . Locus of R is : (A) x^2 + y^2 - 2x + 4y = 0 (B) x^2 + y^2 + 2x + 4y = 0 (C) x^2 + y^2 - 2x - 4y=0 (D) x^2 + y^2 + 2x - 4y = 0

The lines 3x+4y=9&4x-3y+12=0 intersect at Pdot The first line intersects x-a xi s at A and the second line intersects y-a xi s at Bdot Then the circumradius of the triangle P A B is 3/2 (b) 5/2 (c) 10 (d) none

A line intersects x-axis at A(2, 0) and y-axis at B(0, 4) . A variable lines PQ which is perpendicular to AB intersects x-axis at P and y-axis at Q . AQ and BP intersect at R . The locus of R and the circle x^2 + y^2 - 8y - 4 = 0 (A) touch each other internally (B) touche the given circle externally (C) intersect in two distinct points (D) neither intersect nor touch each other