If `x^2 + y^2 - (2lamda + 1)x + (lamda - 7)y + 10 = 0` passes through two fixed points A & B and angle between tangents at A and B is 90°. Then

Consider the family of circles x^(2)+y^(2)-2x-2ay-8=0 passing through two fixed points A and B . Also, S=0 is a cricle of this family, the tangent to which at A and B intersect on the line x+2y+5=0 . The distance between the points A and B , is

Consider the family of circles x^(2)+y^(2)-2x-2ay-8=0 passing through two fixed points A and B . Also, S=0 is a cricle of this family, the tangent to which at A and B intersect on the line x+2y+5=0 . The distance between the points A and B , is

Consider the family of circles x^(2)+y^(2)-2x-2ay-8=0 passing through two fixed points A and B . Also, S=0 is a cricle of this family, the tangent to which at A and B intersect on the line x+2y+5=0 . The distance between the points A and B , is

If a,b,c in GP then the line a^(2)x+b^(2)y+ac=0 always passes through the fixed point

Show that the straight line (a+2b)x+(a-3b)y+b-a=0 always passes through a fixed point , find the cootdinates of that fixed point.

If the lines (1 -x )/(3) = ( 7y - 14)/(2 lamda) = (z - 3)/(2) "and" (7 - 7x)/(3lamda) = (y - 5)/(1) = ( 6 - z ) /(5) are at right angle, then the value of lamda is

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is