List of top Mathematics Questions on Coordinate Geometry asked in IISER

यदि रेखा l1 बिन्दु(1, 1, 1) व बिन्दु(3, 1, 3) को जोड़ती है तथा रेखा l2 बिन्दु(0, 2, −1) व बिन्दु(2, 0, 3) को जोड़ती है, तो रेखा l1 तथा l2 के बीच का कोण क्या है?

Let $\mathcal{C}$ be the set of all the circles in a plane. If \[ \mathcal{R} = \{(C_1, C_2) \in \mathcal{C} \times \mathcal{C} \mid C_1 \text{ and } C_2 \text{ intersect}\} , \] then which of the following statements is TRUE?

Let $\ell$ be the tangent line to the ellipse $x^2 + 16y^2 = 4$ at $\left(1, \frac{\sqrt{3}}{4}\right)$. What is the equation of the line perpendicular to $\ell$ passing through $(2, 0)$?

Consider the following lines in the $XY$-plane:
$L_1 : 5x - 2y = 1$,
$L_2 :$ the line passing through $(0, 1)$ and $(100, 101)$,
$L_3 :$ the line passing through $(1, 11)$ and parallel to the vector $-\hat{i} + 2\hat{j}$.
Let $A = (L_1 \cap L_2) \cup (L_2 \cap L_3) \cup (L_3 \cap L_1)$. What is the total number of elements of $A$?

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

In the given figure, the angles $\angle BAQ = \angle CPQ = \angle CBQ = \frac{\pi}{2}$; and the lengths $QA = 3$ unit, $AB = 4$ unit, and $BC = 1$ unit. What is the length of $PQ$? }