Embibe Experts Solutions for Exercise 4: EXERCISE 11.4

$(1,2)$ are the co-ordinates of a point referred to a rectangular Cartesian coordinate system. The axes are rotated through an angle $45°$ in the positive sense without changing the origin. Then the co-ordinates of the point in the new system is

The co-ordinates of a point $P$ referred to a rectangular co-ordinate system where $O$ is the origin are $(1,-2)$. The axes are rotated about $O$ through an angle $\theta$. If the co-ordinates of $P$ in the new system are $(k-1, k+1)$, then $k^2$ is equal to

Centroid of the triangle, the equations of whose sides are $12x^2-20xy+7y^2=0$ and $2x-3y+4=0$ is

The line joining two points $A(2,0), B(3,1)$ is rotated about $A$ in the counter-clockwise sense through an angle $15°$. If $B$ goes to $C$ in the new position, then co-ordinates of $C$ is

The equations of the diagonals of the square formed by the pairs of straight lines $3x^2+8xy-3y^2=0$ and $3x^2+8xy-3y^2+2x-4y-1=0$ are

Keeping the origin fixed, the coordinate axes are rotated through an angle $\theta$. If the equation of the line $\frac{x}{a}+\frac{y}{b}=1$ with respect to new axes is $\frac{x}{p}+\frac{y}{q}=1$, then

The equation of the lines through the origin and which are perpendicular to the pair of straight lines $x^2-3xy+2y^2=0$ is

The value of $h$ for which $3x^2-2hxy+4y^2=0$ represents a pair of coincident lines are