Amit M Agarwal Solutions for Chapter: Cartesian System of Rectangular Coordinates, Exercise 3: Entrances Gallery

The points $\left(0,\frac{8}{3}\right), \left(1,3\right)$ and $\left(82,30\right)$ are 

The locus of a point which moves so that its distance from $X$-axis is double of its distance from $Y$-axis, is

The three distinct points $A\left(a{t}_1^2,2a{t}_1\right), B\left(a{t}_2^2,2a{t}_2\right)$ and $C(0,a)$ (where $a$ is a real number) are collinear, if

If the distance between $(2,3)$ and $(-5,2)$ is equal to the distance between $(x, 2)$ and $(1,3)$, then the values of $x$ are

If the three points $(0,1),(0,-1)$ and $(x, 0)$ are vertices of an equilateral triangle, then the values of $x$ are

If the three points $(3q,0), (0,3p)$ and $(1,1)$ are collinear, then which one is true?

The area (in sq. units) of the triangle formed by the points $(2,2),(5,5)$ and $(6,7)$ is

$Q, R$ and $S$ are points on the line joining the points $P\left(a,x\right)$ and $T\left(b,y\right)$ such that $PQ=QR=RS=ST,$ then $\left(\frac{5a+3b}{8},\frac{5x+3y}{8}\right)$ is the mid-point of the line segment