Curves `(x-1) (y-2)=5 and (x-1)^(2)+(y+2)^(2)=r^(2)` intersect at four points, A, B, C and D. If centroid of `DeltaABC` lies on line `y=3x-4`, then find the locus of point D.

(x-1)(y-2)=5 and (x-1)^2+(y+2)^2=r^2 intersect at four points A, B, C, D and if centroid of triangle ABC lies on line y = 3x-4 , then locus of D is

Let C be a curve which is the locus of the point of intersection of lines x=2+m and m y=4-mdot A circle s-=(x-2)^2+(y+1)^2=25 intersects the curve C at four points: P ,Q ,R ,a n dS . If O is center of the curve C , then O P^2+O P^2+O R^2+O S^2 is 50 (b) 100 (c) 25 (d) (25)/2

C_(1):x^(2)+y^(2)=r^(2)and C_(2):(x^(2))/(16)+(y^(2))/(9)=1 interset at four distinct points A,B,C, and D. Their common tangents form a parellelogram A'B'C'D'. if A'B'C'D' is a square, then r is equal to

If the points A(2, 2), B(-2, -3), C(1, -3) and D(x, y) form a parallelogram then find the value of x and y.

If the curves x^(2)-y^(2)=4 and xy = sqrt(5) intersect at points A and B, then the possible number of points (s) C on the curve x^(2)-y^(2) =4 such that triangle ABC is equilateral is

The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the center of the circle lies on x-2y=4. The radius of the circle is

If the points P(6,2) and Q(-2,1) and R are the vertices of a DeltaPQR and R is the point on the locus of y=x^(2)-3x+4 , then find the equation of the locus of centroid of DeltaPQR .

If the curves (x^2)/4+y^2=1 and (x^2)/(a^2)+y^2=1 for a suitable value of a cut on four concyclic points, the equation of the circle passing through these four points is (a) x^2+y^2=2 (b) x^2+y^2=1 (c) x^2+y^2=4 (d) none of these