Question

(19) If (x, y) and (y, x) are the coordinates of the same point, then
A. X=0, y = 3
B. X= 3. y = -3
C. X = -3. y = 3
D. X = 3. y = 3​

Answer 1

Answer:

a2−b2=p2−q2

a2+b2=p2+q2

a2+p2=b2+q2

a2b2=p2q2

Answer :

B

Solution :

Suppose one set of rectangular axes is obtained by rotating the coordinate axes of the other set by an angle θ in anticlocwise sense. Let (x,y) be the coordinates of the point with respect to odd axes and (X,Y) be the coordinates with respect to the axes. then,

x=Xcosθ−Y=Xsinθcosθ,

∴ax+by=a(Xcosθ−Ysinθ)+b(Xsinθ+Ycosθ)

⇒ax+by=(acosθ+bsinθ)X+(bcosθ−sinθ)Y

It is given that ax+by becomes pX+qY

∴P=acosθ+bsinθandq=bcosθ−asinθ

⇒p2+q2=(acosθ+bsinθ)2+(bsinθ−asinθ)