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x=a cos( theta) + b sin(theta) y=a sin(theta) – b cos( theta) prove that y*y2-x*y1+y=0

x=a cos(theta) + b  sin(theta)
y=a sin(theta) – b cos(theta)
prove that y*y2-x*y1+y=0

Grade:12

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

x = acos\theta +bsin\theta
y = asin\theta - bcos\theta
x^{2} + y^{2} = a^{2} + b^{2}

Differentiate
2x + 2yy' = 0
yy' + x = 0
y' = -\frac{x}{y}
Differentiate
y'' = -\frac{y-xy'}{y^{2}}
y^{2}y'' = -y+xy'
y^{2}y''-xy' + y = 0
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

x = acos(theta) + bsin(theta)
y = asin(theta) – bcos(theta)
X^2 + y^2 = a^2 + b^2
differentiate
2x + 2yy’ = 0
y’ = – x/y
differentiate
y’’ = – ( y – xy’)/y^2
y^2y’’ = –y + xy’
y’’y^2 –xy’ + y = 0

Thanks and Regards

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