2 If the area of the triangle included between the axes and any tangent to the curve xny = an - Maths - Application of Derivatives

Question

2 If the area of the triangle included between the axes and any
tangent to the curve xny = an is constant ,
then n=
1 1
2 2
3 3/2
4 1/2
Correct ans is1 Plz exp
​

Brijendra Pal · Accepted Answer

Dear Student, Differentiating the above equation, we get xndydx+nyxnn-1= 0 dydx=-nyxThis is slope Now let the point on the graph is x= p , Then pny= any = anpnSo equation of tangent is y-anpn= -n×anpnpx-p y-anpn= -n×anpn+1x-pNow at x = 0y =anpn+nanpn= n+1 anpnand at y = 0 , x-p =-anpn×pn+1-nan= pnx=  p+pn= pn+1nNow area = 12×pn+1n×n+1 anpnIt is constant So value of n must not vary and Also n cannot be equal to 0 as then expression will make undefined so for constant area n = 1You may varify that constant area =12×p1+11×1+1 a1p1 = 2aRegards

2.If the area of the triangle included between the axes and any tangent to the curve xny = an is constant , then n=1.1 2.23.3/24.1/2Correct ans is1. Plz exp. ​

2.If the area of the triangle included between the axes and any tangent to the curve xⁿy = aⁿ is constant , then n=
1.1
2.2
3.3/2
4.1/2
Correct ans is1. Plz exp.