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

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

P(x, y) moves such that the area of the triangle with vertices at P(x, y), (1, -2), (-1, 3) is equal to the area of the triangle with vertices at P(x, y), (2, -1), (3, 1). The locus of P is

The graphs of the equations 2x+3y=11 and x-2y+12=0 intersects at P(x_1,y_1) and the graph of the equation x-2y+12=0 intersects the x-axis at Q(x_2,y_2) . What is the value of (x_1-x_2+ y_1+y_2) ? समीकरणों 2x+3y=11 तथा x-2y+12=0 के आरेख एक दूसरे को P(x_1,y_1) पर काटते ह तथा समीकरण x-2y+12=0 का आरेख x-अक्ष को Q(x_2,y_2) पर काटता है| (x_1-x_2+ y_1+y_2) का मान क्या है?

If theta is the acute angle between the lines with slopes m1 and m2 then tan theta=(m_(1)-m_(2))/(1+m_(1)m_(2)) 2) if p is the length the perpendicular from point P(x1,y1) to the line ax +by+c=0 then p=(ax_(1)+by_(1)+c)/(sqrt(a^(2)+b^(2)))

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

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.