Question

Equation of the tangent line at y=a/4 to the curve y(x^2+a^2)=ax^2 is

Answer 1

Step-by-step explanation:

d/ dx (×2+xy + y²)= d/ dx 3 = 0

BREAK THE LEFT SIDE INTO SEPARTE TERMS:

d/ d× (×2)= 2x

d/ dx (xy) = x d y + / dx + y dx/ dx = x dy/ dx +y

dy / dx (y²) = 2x d y / dx

SO THE WHOLE LEFT SIDE IS:

2x+x dy/ dx + y + 2x d y / dx WHICH EQUALS 0

GATHER TERMS AND SOLVE FOR d y / dx:

x dy/ dx + 2y dy / dx = 2x—y

dy/ dx (x + 2y ) = - (2x+y)

dy/ dx = - (2x + y ) / ( x + 2y )

PLUG THE POINT (1.1) INTO THE EXPRESSION FOR dy/ dx

dy/ dx – (2+1) / (1+2)= 3/3 =- 1 answer i hope helpful ♡