The number of normals to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` from an external point, is

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point

Show that the equation of the normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (a sqrt(2),b) is ax+b sqrt(2)y=(a^(2)+b^(2))sqrt(2)

The point (at^(2),2bt) lies on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 for

The locus of the point of intersection of the tangents at the end-points of normal chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , is

The coordinates of the point at which the line 3x+4y=7 is a normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, are

The number of tangents and normals to the hyperbola (x^(2))/(16)-(y^(2))/(25)=1 of the slope 1 is