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`

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

From a point P, two tangents PA and PB are drawn to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . If these tangents cut the coordinates axes at 4 concyclic points, then the locus of P is

If y=mx+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 m_(1)&m_(2) are the slopes of the tangents to the hyperbola (x^(2))/(25)-(y^(2))/(16)=1 which passes through the point (4,2), find the value of (i)m_(1)+m_(2)&(ii)m_(2)m_(2)

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:

[If m_(1) and m_(2) are slopes of tangents to the hyperbola (x^(2))/(25)-(y^(2))/(16)=1 which pass through the point (6,2) then (11m_(1)m_(2))/(10)=

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.

Tangents at any point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 cut the axes at A and B respectively,If the rectangle at OAPB (where O is origin) is completed then locus of point P is given by