Straight Lines and Pair of Straight Lines · Mathematics · IAT (IISER)

Consider the following lines in the $X Y$-plane:

$$ L_1: 5 x-2 y=1 $$

$L_2$ : The line passing through $(0,1)$ and $(100,101)$,

$L_3$ : The line passing through $(1,11)$ and parallel to the vector $-\hat{\imath}+2 \hat{\jmath}$.

Let $A=\left(L_1 \cap L_2\right) \cup\left(L_2 \cap L_3\right) \cup\left(L_3 \cap L_1\right)$. What is the total number of elements of $A$ ?

Let $A$ be the set of points in the $X Y$-plane which are equidistant from $P(-1,0)$ and $Q(1,0)$. Let $B$ be the set of points in the $X Y$-plane which are equidistant from $A$ and $Q$. If $(5, y)$ is a point in $B$, then what is the value of $y^2$ ?

Let $S=\{(a, b): a, b \in Q\}$ and $\ell$ be the line $y=m x+c$. Which of the following statements is not correct?