Combining transformations - class-X
Description: combining transformations | |
Number of Questions: 17 | |
Created by: Supriya Thakkar | |
Tags: transformations vectors and transformations maths |
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
The area of triangle formed by the lines $x+y-3=0$, $x-3y+9=0$ and $3x-2y+1=0$ is:
if the equation $4{x^2} + 2xy + 2{y^2} - 1 = 0$ becomes $5{x^2} + {y^2} = 1,$ when the axes are rotate through an angle ${45^ \circ }\,$ , then the original equation of the curve is :
If the axes are shifted to $(-2, -3)$ and rotated $\dfrac{\pi}{4}$ then Transformed equation of $2x^{2}+4xy-5y^{2}+20x-22y-14=0$ is
The point $A(2, 1)$ is translated parallel to the line $x- y = 3$ by a distance $4$ units. If the new position $A'$ is in third quadrant, then the coordinates of $A'$ are
If the axes are rotated through an angle of ${30}^{o}$ in the anti-clockwise direction, the coordinates of point $(4,-2\sqrt{3})$ with respect to new axes are-
Let $\displaystyle A=(1,0)$ and $\displaystyle B=(2,1).$ The line $AB$ turns about $A$ through an angle $ \dfrac{\pi}6$ in the clockwise sense, and the new position of $B$ is $B'$. Then $B'$ has the coordinates
The transformed equation of $3{ x }^{ 2 }+3{ y }^{ 2 }+2xy=2$. When the coordinate axes are rotated through an angle of $45$, is