AP EAMCET202018 Sep 2020Morning ShiftMathematicsHyperbolaActual
The equation of the normal to the curve (x=a (t), y=b (t) ) at any point (t ) is
Options
- A(a x+b y=a^2+b^2 )
- B(a x sech (t)+b y cosech (t)=a^2+b^2 )
- C(a x sech (t)-b y cosech (t)=a^2-b^2 )
- D( a x (t) + b y (t) =a^2+b^2 )
Correct answer
B. (a x sech (t)+b y cosech (t)=a^2+b^2 )
Step-by-step solution
Given curve, (x=a h (t) ) and (y=b h (t) ) represents, ( x^2 a^2 - y^2 b^2 =1 ) is a hyperbola and equation of normal at a point ' (t ) ' is ( aligned & x-a t a t a^2 =- y-b t b h t b^2 & a x sech t+b y cosech t=a^2+b^2 aligned )