Tag: vectors and transformations
Questions Related to vectors and transformations
When the axes are rotated through an angle $\dfrac{\pi}{6}$ , find the new coordinate for $(1,0)$
The point to which is shifted in order to remove the first degree terms in $ 2x^{ 2 }+5xy+3y^{ 2 }+6x+7y+1=0 $ is
If the transformed equation of a curve is $9x^{2}+16y^{2}=144$ when the axes rotated through an angle of $45^{o}$ then the original equation of a curve is:
By translating the axes the equation $xy-x+2y=6$ has changed to $XY=C$, then $C=$
lf the axes are translated to the point $(-2, -3)$ , then the equation $\mathrm{x}^{2}+3\mathrm{y}^{2}+4\mathrm{x}+18\mathrm{y}+30=0$ transforms to
lf the origin is shifted to the point $(-1, 2)$ without changing the direction of axes, the equation ${x}^{2} -{y}^{2}+2{x}+4{y}=0$ becomes
lf the axes are rotated through an angle $60^{\mathrm{o}}$, then the transformed equation of $\mathrm{x}^{2}+\mathrm{y}^{2}=25$ is
The transformed equation of $\mathrm{x}\mathrm{c}\mathrm{o}\mathrm{s}\alpha+\mathrm{y}\mathrm{s}\mathrm{i}\mathrm{n}\alpha = \mathrm{P}$ when the axes are rotated through an angle $\alpha$ is
When axes are rotated by an angle of $135^{0}$, initial coordinates of the new coordinate $(4, -3)$ are
The point $(4,3)$ is translated to the point $(3,1)$ and then axes are rotated through $30^{\mathrm{o}}$ about the origin, then the new position of the point is