If the roots of the equation `(x_1^2-a^2)m^2-2x_1y_1m+y1^2+b^2=0` are the slopes of two perpendicular lines intersecting at P, then locus of P is

If the roots of the equation (x_(1)^(2)-a^(2))m^(2)-2x_(1)y_(1)m+y_(1)^(2)+b^(2)=0 are the slopes of two perpendicular lines intersecting at P(x_(1), y_(1)) then the locus of P is

If the roots of the equation (x_(1)^(2)-a^2)m^2-2x_1y_1m+y_(1)^(2)+b^2=0(agtb) are the slopes of two perpendicular lies intersecting at P(x_1,y_1) , then the locus of P is

If the roots of the equation (x_(1)^(2)-a^2)m^2-2x_1y_1m+y_(1)^(2)+b^2=0(agtb) are the slopes of two perpendicular lies intersecting at P(x_1,y_1) , then the locus of P is

If the roots of the equation (x_(1)^(2)-a^2)m^2-2x_1y_1m+y_(1)^(2)+b^2=0(agtb) are the slopes of two perpendicular lies intersecting at P(x_1,y_1) , then the locus of P is

If the roots of the equation (x_(1)^(2)-a^2)m^2-2x_1y_1m+y_(1)^(2)+b^2=0(agtb) are the slopes of two perpendicular lies intersecting at P(x_1,y_1) , then the locus of P is

If the roots of the equation (x_(1)^(2)-16)m^(2)-2x_(1)y_(1)m+y_(1)^(2)+9=0 are the slopes of two perpendicular lines intersecting at p(x_(1),y_(1)) then the locus of p is

If the roots of the equation ( x _ 1 ^ 2 - a ^ 2 ) m ^ 2 - 2x _ 1 y _ 1 m + ( y _ 1 ^ 2 + b ^ 2 ) = 0 , ( a gt b ) are the slopes of two perpendicular lines intersecting at P (x _ 1, y _ 1 ) , then the locus of P is

Equation x^(2)+m_(1)y^(2)+m_(2)xy=0 jointly represents a pair of perpendicular lines if

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