AP EAPCET 2021 (19-Aug Afternoon)

When the coordinate axes are rotated through an angle $135°$, the coordinates of a point $P$ in the new system are known to be $(4,-3)$. Then find the coordinates of $P$ in the original system.

If $A(4,7), B(-7,8)$ and $C(1,2)$ are the vertices of $∆ABC$, then the equation of perpendicular bisector of the side $AB$ is

If the points $(2,4,-1),(3,6,-1)$ and $(4,5,1)$ are three consecutive vertices of a parallelogram, then its fourth vertex is

The points $(2,3,4),(-1,-2,1)$ and $(5,8,7)$ are

Find the equation of a line which passes through $\left(2{\cos }^3\theta ,2{\sin }^3\theta \right)$ and is perpendicular to the line $x\cos \theta -y\sin \theta =2\cos 2\theta$.

If the orthocenter of the triangle formed by the lines $2x+3 y-1=0, x+2y+1=0$ and $ax+by-1=0$ lies at origin, then $\frac{1}{a}+\frac{1}{b}=$

Given two fixed points $A(-2,1)$ and $B(3,0)$, find the locus of a point $P$ which moves such that the angle $\angle APB$ is always a right angle.

The ratio in which the straight line $3x+4y=6$ divides the join of the points $(2,-1)$ and $(1,1)$ is