Embibe Experts Solutions for Exercise 6: Assignment

A variable straight line, drawn through the point of intersection of the straight line $\frac{x}{4}+\frac{y}{2}=1$ and $\frac{x}{2}+\frac{y}{4}=1$ meets the co-ordinate axes in $A$ and $B$. The locus of midpoint of $AB$ is

A straight line passes through a fixed point $(2,3)$. Locus of the foot of the perpendicular on it drawn from the origin is

$y=mx$ be a variable line ($m$ is variable) intersect the lines $2 x+y-2=0$ and $x-2 y+2=0$ in $P$ and $Q$. The locus of midpoint of segment of $PQ$. is

A variable straight line passes through the points of intersection of the lines $x+2 y=1$ and $2 x-y=1$ and meets the co-ordinate axes in $A$ and $B$. The locus of middle point of $AB$ is

If $A(\cos \alpha ,\sin \alpha ),B(\sin \alpha ,-\cos \alpha ),C(2,1)$ are vertices of a triangle $ABC$. The locus of its centroid if $\alpha$ varies is

Two fixed points $A$ and $B$ have co-ordinates $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right).$ A point $P$ moves such that $AP$ is perpendicular to $BP$, then locus of $P$ is

Locus of the middle point of the intercept on the line  $y=x+c$  made by the lines $2 x+3 y=5$ and $2 x+3 y=8, c$ being a parameter, is -

If the pair of straight lines $x^2-y^2+2x+1=0$ meet the $y$-axis in $A$ and $B,|A B|$ equals to