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

x =a tan theta ,y =b sec 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 -

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 x=acos theta ,y=b sin theta,then b^(2)x^(2)+a^(2)y^(2)-a^(2)b^(2) is equal to:

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

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

Match the following {:("parametric equation","Cartesian equation"),(" List - I"," List - II"),("1) "x cos theta + y sin theta =a",","a) "(x^(2)-y^(2))^(2)=16xy),(" "x sin theta - y cos theta = b,),("2) "x=sec theta + tan theta",","b) "xy=1),(" "y=sec theta - tan theta,),("3) "xsec theta + y tan theta =a",","c) "x^(2)-y^(2)=a^(2)-b^(2)),(" "x tan theta + y sec theta = b,),("4) "x=cot theta + cos theta",","d) "x^(2)+y^(2)=a^(2)+b^(2)),(" "y=cot theta - cos theta,):}

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