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_(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)-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+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 , ( a gt b ) are the slopes of two perpendicular lines intersecting at P (x _ 1, y _ 1 ) , then the locus of P is

A normal to (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets the axes in L and M . The perpendiculars to the axes through L and M intersect at P .Then the equation to the locus of P is

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 m_1,m_2 " are the roots of the equation " x^2-ax-a-1=0 , then the area of the triangle formed by the three straight line y=m_1,x,y=m_2x and y=a(ane -1) is

If two tangents drawn to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 intersect perpendicularly at P, then the locus of P is a circle x^(2)+y^(2)=a^(2)+b^(2) . The circle is called

If two tangents drawn to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 intersect perpendicularly at P. then the locus of P is a circle x^(2)+y^(2)=a^(2)+b^(2) the circle is called

If two tangents drawn to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 intersect perpendicularly at P. then the locus of P is a circle x^(2)+y^(2)=a^(2)+b^(2) the circle is called