If `(x_1, y_1)&(x_2, y_2)` are the ends of diameter of a circle such that `x_1&x_2` are the roots of the equation `a x^2+b x+c=0` and `y_1&y_2` are the roots of the equation `p y^2+q y+c=0` . Then the coordinates f the centre of the circle is: `(b/(2a), q/(2p))` (b) `(-b/(2a),=q/(2p))` `(b/a , q/p)` (d) None of these

If (x_1, y_1)&(x_2,y_2) are the ends of a diameter of a circle such that x_1&x_2 are the roots of the equation a x^2+b x+c=0 and y_1&y_2 are the roots of the equation p y^2=q y+c=0. Then the coordinates of the centre of the circle is: (b/(2a), q/(2p)) ( b/(2a), q/(2p)) (b/a , q/p) d. none of these

If (x_(1),y_(1))&(x_(2),y_(2)) are the ends of a diameter of a circle such that x_(1)&x_(2) are the roots of the equation ax^(2)+bx+c=0 and y_(1)&y_(2) are the roots of the equation py^(2)=qy+c=0. Then the coordinates of the centre of the circle is: ((b)/(2a),(q)/(2p))(-(b)/(2a),(q)/(2p))((b)/(a),(q)/(p)) d.none of these

If a, b are the roots of equation x^(2)-3x + p =0 and c, d are the roots of x^(2) - 12x + q = 0 and a, b, c, d are in G.P., then prove that : p : q =1 : 16

The abscissa of two points A and B are the roots of the equation x^(2)+2ax-b^(2)=0 and their ordinates are the roots of y^(2)+2py-q^(2)=0 then the distance AB in terms of a,b,p,q is

Let a ,b , c ,p ,q be real numbers. Suppose alpha,beta are the roots of the equation x^2+2p x+q=0,alphaa n d1//beta are the roots of the equation a x^2+2b x+c=0,w h e r ebeta^2 !in {-1,0,1}dot Statement 1: (p^2-q)(b^2-a c)geq0 Statement 2: b!=p aorc!=q a

Let a ,b , c ,p ,q be real numbers. Suppose alpha,beta are the roots of the equation x^2+2p x+q=0,alphaa n d1//beta are the roots of the equation a x^2+2b x+c=0,w h e r ebeta^2 !in {-1,0,1}dot Statement 1: (p^2-q)(b^2-a c)geq0 Statement 2: b!=p aorc!=q a

If alpha,beta are the roots of a x^2+b x+c=0a n dalpha+h ,beta+h are the roots of p x^2+q x+r=0then h= a. -1/2(a/b-p/q) b. (b/a-q/p) c. 1/2(b/a-q/p) d. none of these

If p and q are the roots of the equation x^2-p x+q=0 , then p=1,\ q=-2 (b) b=0,\ q=1 (c) p=-2,\ q=0 (d) p=-2,\ q=1

If the equation p x^2+(2-q)x y+3y^2-6q x+30 y+6q=0 represents a circle, then find the values of p and q .

If the equation p x^2+(2-q)x y+3y^2-6q x+30 y+6q=0 represents a circle, then find the values of p and q .