two tangents of a hyperbola `x^2/a^2 - y^2/b^2 = 1` having m1m2 cuts the axes at 4 concyclic points .find value of m1 m2

Two tangents to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 having m_1a n dm_2 cut the axes at four concyclic points. Fid the value of m_1m_2dot

If y=m x+c is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, having eccentricity 5, then the least positive integral value of m is_____

If y=m x+c is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, having eccentricity 5, then the least positive integral value of m is_____

Two tangents to the hyperbola (x^(2))/(25) -(y^(2))/(9) =1 , having slopes 2 and m where (m ne 2) cuts the axes at four concyclic points then the slope m is/are

If (m_i,1/m_i),i=1,2,3,4 are concyclic points then the value of m_1m_2m_3m_4 is

The point of intersection of tangents drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at the points where it is intersected by the line l x+m y+n=0 , is ((-a^2l)/n ,(b^2m)/n) (b) ((-a^2l)/m ,(b^2n)/m) ((a^2l)/m ,(-b^2n)/m) (d) ((a^2l)/m ,(b^2n)/m)

The point of intersection of tangents drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at the points where it is intersected by the line l x+m y+n=0 is

Statement 1 : If from any point P(x_1, y_1) on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 , tangents are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, then the corresponding chord of contact lies on an other branch of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 Statement 2 : From any point outside the hyperbola, two tangents can be drawn to the hyperbola.

The values of 'm' for which a line with slope m is common tangent to the hyperbola x^2/a^2-y^2/b^2=1 and parabola y^2 = 4ax can lie in interval:

The tangent at any point P on the circle x^2 + y^2 = 2 cuts the axes in L and M . Find the locus of the middle point of LM .