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`

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

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

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

Three sides of a triangle are represented by lines whose combined equation is (2x+y-4) (xy-4x-2y+8) = 0 , then the equation of its circumcircle will be : (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

y-1=m_1(x-3) and y - 3 = m_2(x - 1) are two family of straight lines, at right angled to each other. The locus of their point of intersection is: (A) x^2 + y^2 - 2x - 6y + 10 = 0 (B) x^2 + y^2 - 4x - 4y +6 = 0 (C) x^2 + y^2 - 2x - 6y + 6 = 0 (D) x^2 + y^2 - 4x - by - 6 = 0

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 (a)3x-4y+2=0 (b)4x+3y+7=0 (c)6x-8y+7=0 (d) none of these

The tangent from the point of intersection of the lines 2x – 3y + 1 = 0 and 3x – 2y –1 = 0 to the circle x^(2) + y^(2) + 2x – 4y = 0 is