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_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+y1^(2)+b^(2)=0 are the slopes of two perpendicular lines intersecting at P, then locus of P is

If m_(1),m_(2) are the slopes of tangents to the ellipse S=0 drawn from (x_(1),y_(1)) then m_(1)+m_(2)

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

The length of tangent at a point P(x_(1),y_(1)) to the curve y=f(x) ,having slope m at 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

Two point B(x_(1), y_(1)) and C(x_(2), y_(2)) are such that x_(1), x_(2) are the roots of the equation x^(2)+4x+3=0 and y_(1),y_(2) are the roots of the equation y^(2)-y-6=0 . Also x_(1)lt x_(2) and y_(1)gt y_(2) . Coordinates of a third point A are (3, -5). If t is the length of the bisector of the angle BAC, then l^(2) is equal to.

If m_(1),m_(2) be the roots of the equation x^(2)+(sqrt(3)+2)x+sqrt(3)-1 =0 , then the area of the triangle formed by the lines y = m_(1)x,y = m_(2)x and y = 2 is

Locus of the points of intersection of perpendicular tangents to x^(2)/9 - y^(2)/16 = 1 is

If the point x_(1)+t(x_(2)-x_(1)),y_(1)+t(y_(2)-y_(1)) divides the join of (x_(1),y_(1)) and (x_(2),y_(2)) internally then locus of t is