" (e) "(x^(2))/(a^(2))-(y^(2))/(b^(2))=1,quad " at "(a sec theta,b tan theta)

Find the equations of tangent and normal to the curve (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at (a sec theta, b tan theta)

Find the equation of tangent at the specified point on the following curve : (x^(2))/(a^(2))-(y^(2))/(b^(2))=1" at"( a sec theta, b tan theta)

The slop of the normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( a sec theta , b tan theta) is -

x = a sec theta, y = b tan theta .

If the line y = mx + sqrt(a^(2)m^(2) - b^(2)) touches the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 at the point (a sec theta, b tan theta) , then find theta .

If (a sec theta, b tan theta) and (a sec phi, b tan phi) are the ends of a focal chord of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , then prove that tan.(theta)/(2)tan.(phi)/(2)=(1-e)/(1+e) .

Prove that b^(2)x^(2)-a^(2)y^(2)=a^(2)b^(2) , if x=a sec theta,y=b tan theta

If the chord joining the points (a sec theta_(1),b tan theta_(1)) and (a sec theta_(2),b tan theta_(2)) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is a focal chord,then prove that tan((theta_(1))/(2))tan((theta_(2))/(2))+(ke-1)/(ke+1)=0, where k=+-1

Evaluate (y^(2))/(b^(2))-(x^(2))/(a^(2)) , where x= a tan theta and y = b sec theta

Evaluate (y^(2))/(b^(2))-(x^(2))/(a^(2)) , whre x=a tan theta and y= b sec theta .