lf x=acostheta+bsintheta, y=asintheta-b...

lf `x=acostheta+bsintheta`, `y=asintheta-bcostheta` then show that `y^2(d^2y)/dx^2-x dy/dx+y=0`

Verified by Experts

`x=acostheta+bsintheta`
`y=asintheta-bcostheta`
`x^2+y^2=a^2+b^2`
`2x+2yy'=0`
`yy'=-x`
`x+yy'=0`
`1+(y')^2+yy''=0`
`yy''=-1-(y')^2`
...

Similar Questions

Explore conceptually related problems

x=acostheta+bsintheta and y=asintheta-bcostheta, show that y^2(d^2y)/(dx^2)-x(dy)/(dx)+y=0

If x=acostheta+bsintheta,y=asintheta-bcostheta , show : y^(2)(d^(2)y)/(dx^(2))-x(dy)/(dx)+y=0 .

If x=acostheta-bsinthetaandy=asintheta+bcostheta , then show that : x^(2)+y^(2)=a^(2)+b^(2)

If acostheta+bsintheta=m and asintheta-bcostheta=n , then show that a^(2)+b^(2)=m^(2)+n^(2) .

x/acostheta+y/bsintheta=1, x/asintheta-y/bcostheta=1 then x^2/a^2+y^2/b^2=

If acostheta+b sintheta=x and asintheta-bcostheta=y prove that a^2+b^2=x^2+y^2

If x/acostheta+y/bsintheta=1,x/asintheta-y/bcostheta=1 ,' then prove that x/a^2 + y/b^2 =2'