Tag: transformations

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

The ordinate of the point which divides the lines joining the origin and the point $(1,2)  $ externally in the ratio of $3:2$ is

The points (22,23) divides the join of P (7,5) and Q externally in the ratio 3:5, then Q=

The point $(22, 33)$ divides the join of $P(7, 5)$ and $Q$ externally in the ratio $3 : 5$, then coordinates of $Q$ are