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Yukti Vault

Coordinate Geometry

Points and Straight Lines: JEE Main & Advanced PYQs

284 previous year questions on Points and Straight Lines from JEE Main and JEE Advanced papers, each with its exam and year, an answer and a solution.

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Questions 201-250 of 284

  1. Locus of mid point of the portion between the axes of $x\cos\alpha+y\sin\alpha=p$ where $p$ is constant is
  2. If $x_1,x_2,x_3$ as well as $y_1,y_2,y_3$ are in G.P. with the same common ratio, then the points $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3)$
  3. The diagonals of a parallelogram $PQRS$ are along the lines $x+3y=4$ and $6x-2y=7$. Then $PQRS$ must be a
  4. A rectangle $PQRS$ has its side $PQ$ parallel to the line $y=mx$ and vertices $P,Q$ and $S$ on the lines $y=a$, $x=b$ and $x=-b$, respectively. Find the locus of the …
  5. The incentre of the triangle with vertices $(1,\sqrt3)$, $(0,0)$ and $(2,0)$ is
  6. The number of integer values of $m$, for which the $x$-coordinate of the point of intersection of the lines $3x+4y=9$ and $y=mx+1$ is also an integer, is
  7. If the vertices $P,Q,R$ of a triangle $PQR$ are rational points, which of the following points of the triangle $PQR$ is (are) always rational point(s)? (A rational point …
  8. Let $PQR$ be a right angled isosceles triangle, right angled at $P(2,1)$. If the equation of the line $QR$ is $2x+y=3$, then the equation representing the pair of lines …
  9. The orthocentre of the triangle formed by the lines $xy=0$ and $x+y=1$ is
  10. Area of the parallelogram formed by the lines $y=mx$, $y=mx+1$, $y=nx$ and $y=nx+1$ equals
  11. Let $PS$ be the median of the triangle with vertices $P(2,2)$, $Q(6,-1)$ and $R(7,3)$. The equation of the line passing through $(1,-1)$ and parallel to $PS$ is
  12. A triangle with vertices $(4,0)$, $(-1,-1)$, $(3,5)$ is
  13. If the pair of lines $ax^{2}+2hxy+by^{2}+2gx+2fy+c=0$ intersect on the $y$ axis then
  14. A straight line through the origin $O$ meets the parallel lines $4x+2y=9$ and $2x+y+6=0$ at points $P$ and $Q$ respectively. Then the point $O$ divides the segment $PQ$ …
  15. The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices $(0,0)$, $(0,21)$ and …
  16. The pair of lines represented by $3ax^{2}+5xy+\left(a^{2}-2\right)y^{2}=0$ are perpendicular to each other for
  17. Orthocentre of triangle with vertices $(0,0)$, $(3,4)$ and $(4,0)$ is
  18. Let $P=(-1,0)$, $Q=(0,0)$ and $R=\left(3,3\sqrt3\right)$ be three points. Then the equation of the bisector of the angle $PQR$ is
  19. Area of the triangle formed by the line $x+y=3$ and angle bisectors of the pair of straight lines $x^{2}-y^{2}+2y=1$ is
  20. The area of the triangle formed by the intersection of a line parallel to the $x$-axis and passing through $P(h,k)$ with the lines $y=x$ and $x+y=2$ is $4h^{2}$. Find …
  21. Let a point $A$ lie between the parallel lines $L_1$ and $L_2$ such that its distances from $L_1$ and $L_2$ are $6$ and $3$ units, respectively. Then the area (in sq. …
  22. Let $A(1,0)$, $B(2,-1)$ and $C\left(\frac73,\frac43\right)$ be three points. If the equation of the bisector of the angle $ABC$ is $\alpha x+\beta y=5$, then the value …
  23. Let the mid points of the sides of a triangle $ABC$ be $\left(\frac{5}{2},7\right)$, $\left(\frac{5}{2},3\right)$ and $(4,5)$. If its incentre is $(h,k)$, then $3h+k$ is …
  24. In an equilateral triangle $PQR$, let the vertex $P$ be at $(3,5)$ and the side $QR$ be along the line $x+y=4$. If the orthocentre of the triangle $PQR$ is …
  25. Let the vertex $A$ of a triangle $ABC$ be $(1,2)$, and the mid-point of the side $AB$ be $(5,-1)$. If the centroid of this triangle is $(3,4)$ and its circumcenter is …
  26. Among the statements $(S_1)$ : If $A(5,-1)$ and $B(-2,3)$ are two vertices of a triangle, whose orthocentre is $(0,0)$, then its third vertex is $(-4,-7)$ and $(S_2)$ …
  27. Let $A(1,2)$ and $C(-3,-6)$ be two diagonally opposite vertices of a rhombus, whose sides $AD$ and $BC$ are parallel to the line $7x-y=14$. If $B(\alpha,\beta)$ and …
  28. Let $ABC$ be an equilateral triangle with orthocenter at the origin and the side $BC$ on the line $x+2\sqrt2y=4$. If the co-ordinates of the vertex $A$ are …
  29. Let the angles made with the positive $x$-axis by two straight lines drawn from the point $P(2,3)$ and meeting the line $x+y=6$ at a distance $\sqrt{\frac23}$ from the …
  30. Let $O(0,0)$, $P(3,4)$, $Q(6,0)$ be the vertices of the triangle $OPQ$. The point $R$ inside the triangle $OPQ$ is such that the triangles $OPR$, $PQR$, $OQR$ are of …
  31. Let $ABCD$ be a quadrilateral with area $18$, with side $AB$ parallel to the side $CD$ and $AB=2\,CD$. Let $AD$ be perpendicular to $AB$ and $CD$. If a circle is drawn …
  32. Lines $L_1: y-x=0$ and $L_2: 2x+y=0$ intersect the line $L_3: y+2=0$ at $P$ and $Q$, respectively. The bisector of the acute angle between $L_1$ and $L_2$ intersects …
  33. Consider three points $P=(-\sin(\beta-\alpha),-\cos\beta)$, $Q=(\cos(\beta-\alpha),\sin\beta)$ and $R=(\cos(\beta-\alpha+\theta),\sin(\beta-\theta))$, where …
  34. A straight line $L$ through the point $(3,-2)$ is inclined at an angle $60^\circ$ to the line $\sqrt3x+y=1$. If $L$ also intersects the $x$-axis, then the equation of …
  35. For a point $P$ in the plane, let $d_1(P)$ and $d_2(P)$ be the distances of the point $P$ from the lines $x-y=0$ and $x+y=0$ respectively. The area of the region $R$ …
  36. The locus of the orthocentre of the triangle formed by the lines $$(1+p)x-py+p(1+p)=0,$$ $$(1+q)x-qy+q(1+q)=0,$$ and $y=0$, where $p\neq q$, is
  37. The straight line $2x-3y=1$ divides the circular region $x^2+y^2\le 6$ into two parts. If …
  38. For $a>b>c>0$, the distance between $(1,1)$ and the point of intersection of the lines $ax+by+c=0$ and $bx+ay+c=0$ is less than $2\sqrt{2}$. Then
  39. A rod of length eight units moves such that its ends $A$ and $B$ always lie on the lines $x-y+2=0$ and $y+2=0$, respectively. If the locus of the point $P$, that divides …
  40. The value of $\lambda^2$ is ___ .
  41. The value of $D$ is ___ .
  42. Equations of the sides $QR$, $RP$ are
  43. Each of the four inequalities given below defines a region in the $xy$ plane. One of these four regions does not have the following property: for any two points …
  44. Match the following: Column I (i) Two rays in the first quadrant $x+y=|a|$ and $ax-y=1$ intersect each other in the interval $a\in(a_0,\infty)$, the value of $a_0$ is …
  45. $ABC$ is a triangle with $\angle B$ greater than $\angle C$. $D$ and $E$ are points on $BC$ such that $AD$ is perpendicular to $BC$ and $AE$ is the bisector of angle …
  46. $ABC$ is a triangle, $P$ is a point on $AB$, and $Q$ is a point on $AC$ such that $\angle AQP=\angle ABC$. Complete the relation $$\frac{\text{area of }\triangle …
  47. In a $\triangle ABC$, $\angle A=90^\circ$ and $AD$ is an altitude. Complete the relation $\dfrac{BD}{BA}=\dfrac{AB}{(\ldots)}$.
  48. Consider the lines given by $L_1: x+3y-5=0$ $L_2: 3x-ky-1=0$ $L_3: 5x+2y-12=0$ Match the Statements / Expressions in Column I with the Statements / Expressions in Column …
  49. $ABC$ is a triangle with $AB=AC$. $D$ is any point on the side $BC$. $E$ and $F$ are points on the sides $AB$ and $AC$, respectively, such that $DE$ is parallel to $AC$ …
  50. The ends $A$, $B$ of a straight line segment of constant length $c$ slide upon the fixed rectangular axes $OX$, $OY$ respectively. If the rectangle $OAPB$ be completed …

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