The line `L_1-=4x+3y-12=0` intersects the x-and y-axies at `Aa n dB ,` 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

Let a given line L_1 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 Rand S, respectively. Show that the locus of the point of intersection of the line PS and QR is a circle passing through the origin

The straight line 2x-3y+5=0 intersects the x -axis and y- axis-

A line passing through the point P(4,2) meets the x and y-axis at A and B respectively. If O is the origin, then locus of the centre of the circumcircle of triangle OAB is

A striaght line intersect x-axis at A(7,0) and y-axis at B(0,-5). The straight line PQ is perpendicular to AB and intersect the x and y-axes at P adn Q respectively. Find the eqution to the locus of the point of intersection of the line AQ and BP.

If the intercepts of the variable circle on the x- and y-axis are 2 units and 4 units, respectively, then find the locus of the center of the variable circle.

A line cuts the x-axis at A(5,0) and the y-axis at B(0,-3). A variable line PQ is drawn perpendicular to AB cutting the x-axis at P and the y-axis at Q. If AQ and BP meet at R, then the locus of R is

The line x+y=p meets the x- and y-axes at Aa n dB , respectively. A triangle A P Q is inscribed in triangle O A B ,O being the origin, with right angle at QdotP and Q lie, respectively, on O Ba n dA B . If the area of triangle A P Q is 3/8t h of the are of triangle O A B , the (A Q)/(B Q) is equal to (a) 2 (b) 2/3 (c) 1/3 (d) 3

A line cuts the x-axis at A (7, 0) and the y-axis at B(0, - 5) A variable line PQ is drawn perpendicular to AB cutting the x-axis in P and the y-axis in Q. If AQ and BP intersect at R, find the locus of R.

The straight line 4x + 3y - 12 = 0 intersects the x -and y-axis A and B respectively. Find the coordinates of the point at which the straight line bar(AB) is divided internally into the ratio 2 : 1.

The straight lines 4x + 3y = 12 and 4x - 3y = 12 intersect the x-axis at A and B respectively. If the lengt of the perpendicular drawn from C to AB be 4 units, then area of the DeltaABC is