The tangent at any point `theta` on the hyperbola `x^2/a^2-y^2/b^2=1` meet the pair of straight lines `b^2x^2 - a^2y^2 = 0` at the points `A` and `B`. Then length of the line segment `AB` is

The tangent to the hyperbola x^2 - y^2 = 3 are parallel to the straight line 2x + y + 8 = 0 at the following points

If the pair of straight lines x^(2)-y^(2)+2x+1=0 meet the y -axis in A and B, AB equals to

If the tangent at a point P on the circle x^2 + y^2 + 6x + 6y = 2 , meets the straight line 5x- 2y + 6 = 0 at a point Q on the y-axis, then the length of PQ is:

The line x+y=k meets the pair of straight lines x^(2)+y^(2)-2x-4y+2=0 in two points A and B. If O is the origin and angleAOB=90^(@) then the value of kgt1 is

If the tangent at the point P on the circle x^2+y^2+6x+6y=2 meets the straight line 5x - 2y + 6 = 0 at a point on the y-axis, then the length of PQ is

The tangent at the vertex of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets its conjugate hyperbola at the point whose coordinates are

If the tangent at the point P on the circle x^2+y^2+6x+6y=2 meets the straight line 5x-2y+6=0 at a point Q on the Y-axis, then the length of PQ is

If the tangent at the point P on the circle x^2+y^2+6x + 6y = 2 meets the straight line 5x- 2y + 6 = 0 at a point Q on the y-axis, then the length of PQ 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