Question

show that the axes are to be rotated through an angle of 1/2 tan -¹(2h/a-b)so as tp remove the xy terms from equation ax²+2hxy+by²=0 is not equal to b through the angle π\4 is a=b​

Answer 1

Answer:

Suppose axes are rotated through an angle θ in the anticlockwise sense.

Let x = X cosθ - Y cos θsin

and y = X sin θ + Y sinθ.

Therefore, the given equation will be transformed to

a(Xcosθ-Ysinθ)2 + 2h(Xcosθ-Ysinθ)(Xsinθ+Ycosθ)+b(Xsinθ+ Ycosθ)2 = 0( cos sin )

In this equation, the coefficient of xy is 0