Question

Find the angle through which the axes are to be rotated so that the equation
x√3+y+6=0 will be reduced to the form x=c. Determine the value of c also.

please solve this asap i need it.​

Answer 1

Answer:

The new form will be,

x=x'cosθ−y'sinθ

y=x' sinθ+y'cosθ

Answer 2

Answer:

[tex]The new form will be, 

x=x′cosθ−y′sinθ

y=x′sinθ+y′cosθ

So putting this value in the equation Ax+By+C=0 we get,

A(x′cosθ−y′sinθ)+B(x′sinθ+y′cosθ)=−C

x′(Acosθ+Bsinθ)+y′(Bcosθ−Asinθ)=−C

For, x′ to be constant, (Bcosθ−Asinθ) must be 0.

So, AB=tanθ

or, θ=tan−1AB

And the constant is, x′=Acosθ+Bsinθ−C

or, x′=(A.A2+B2A)+(B.A2+B2B)−C

or, x′=A2+B2−C