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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 101-150 of 284

  1. A straight line $L$ through the point $(3,-2)$ is inclined at an angle of $60^{\circ}$ to the line $\sqrt3x+y=1$. If $L$ also intersects the $X$-axis, then the equation …
  2. The sides of a rhombus $ABCD$ are parallel to the lines $x-y+2=0$ and $7x-y+3=0$. If the diagonals of the rhombus intersect at $P(1,2)$ and the vertex $A$ (different …
  3. If the incentre of an equilateral triangle is $(1,1)$ and the equation of its one side is $3x+4y+3=0$, then the equation of the circumcircle of this triangle is :
  4. The region represented by $|x-y|\le2$ and $|x+y|\le2$ is bounded by a
  5. A light ray emits from the origin making an angle $30^\circ$ with the positive $x$-axis. After getting reflected by the line $x+y=1$, if this ray intersects the $x$-axis …
  6. Consider the set of all lines $px+qy+r=0$ such that $3p+2q+4r=0$. Which one of the following statements is true?
  7. Let the points of intersections of the lines $x-y+1=0$, $x-2y+3=0$ and $2x-5y+11=0$ are the mid points of the sides of a triangle $ABC$. Then the area of the triangle …
  8. A straight line cuts off the intercepts $OA=a$ and $OB=b$ on the positive directions of $x$-axis and $y$-axis respectively. If the perpendicular from origin $O$ to this …
  9. One side of a rectangle lies along the line $4x+7y+5=0$. Two of its vertices are $(-3,1)$ and $(1,1)$. Find the equations of the other three sides.
  10. A triangle $ABC$ has sides $AB=AC=5$ cm and $BC=6$ cm. Triangle $A'B'C'$ is the reflection of the triangle $ABC$ in a line parallel to $AB$ placed at a distance $2$ cm …
  11. A straight line $L$ is perpendicular to the line $5x-y=1$. The area of the triangle formed by the line $L$ and the coordinate axes is $5$. Find the equation of the line …
  12. A straight line segment of length $\ell$ moves with its ends on two mutually perpendicular lines. Find the locus of the point which divides the line segment in the ratio …
  13. State TRUE or FALSE: The straight line $5x+4y=0$ passes through the point of intersection of the straight lines $x+2y-10=0$ and $2x+y+5=0$.
  14. Let the lines $3x-4y-\alpha=0$, $8x-11y-33=0$, and $2x-3y+\lambda=0$ be concurrent. If the image of the point $(1,2)$ in the line $2x-3y+\lambda=0$ is …
  15. A triangle is formed by $X$-axis, $Y$-axis and the line $3x+4y=60$. Then the number of points $P(a,b)$ which lie strictly inside the triangle, where $a$ is an integer …
  16. Lines are drawn parallel to the line $4x-3y+2=0$, at a distance $\frac35$ units from the origin. Then which one of the following points lies on any of these lines?
  17. Let $ABC$ be a triangle formed by the lines $7x-6y+3=0$, $x+2y-31=0$ and $9x-2y-19=0$. Let the point $(h,k)$ be the image of the centroid of $\Delta ABC$ in the line …
  18. The point $(4,1)$ undergoes the following three transformations successively: reflection about the line $y=x$; translation through a distance $2$ units along the …
  19. The straight lines $x+y=0$, $3x+y-4=0$, $x+3y-4=0$ form a triangle which is
  20. Let $A(1,0)$, $B(6,2)$ and $C\left(\frac32,6\right)$ be the vertices of a triangle $ABC$. If $P$ is a point inside the triangle $ABC$ such that the triangles $APC$ …
  21. The points $(-a,-b)$, $(0,0)$, $(a,b)$ and $\left(a^{2},ab\right)$ are
  22. The area enclosed within the curve $|x|+|y|=1$ is ______.
  23. The set of lines $ax+by+c=0$, where $3a+2b+4c=0$, is concurrent at the point ______.
  24. A triangle has a vertex at $(1,2)$ and the mid points of the two sides through it are $(-1,1)$ and $(2,3)$. Then the centroid of this triangle is :
  25. The equations of the sides $AB$, $BC$ and $CA$ of a triangle $ABC$ are $2x+y=0$, $x+py=21a$ ($a\neq0$) and $x-y=3$ respectively. Let $P(2,a)$ be the centroid of the …
  26. If a straight line passing through the point $P(-3,4)$ is such that its intercepted portion between the coordinate axes is bisected at $P$, then its equation is :
  27. (a) Two vertices of a triangle are $(5,-1)$ and $(-2,3)$. If the orthocentre of the triangle is the origin, find the coordinates of the third point. (b) Find the …
  28. A straight line $L$ at a distance of $4$ units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes …
  29. If the sum of squares of all real values of $\alpha$, for which the lines $2x-y+3=0$, $6x+3y+1=0$ and $\alpha x+2y-2=0$ do not form a triangle is $p$, then the greatest …
  30. The area of a triangle is $5$. Two of its vertices are $A(2,1)$ and $B(3,-2)$. The third vertex $C$ lies on $y=x+3$. Find $C$.
  31. If $x_1,x_2,x_3$ and $y_1,y_2,y_3$ are both in G.P. with the same common ratio, then the points $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3,y_3)$ :
  32. A straight line through origin $O$ meets the lines $3y=10-4x$ and $8x+6y+5=0$ at points $A$ and $B$ respectively. Then, $O$ divides the segment $AB$ in the ratio
  33. If the three distinct lines $x+2ay+a=0$, $x+3by+b=0$ and $x+4ay+a=0$ are concurrent, then the point $(a,b)$ lies on a :
  34. Let $A(2,-3)$ and $B(-2,1)$ be vertices of a triangle $ABC$. If the centroid of this triangle moves on the line $2x+3y=1$, then the locus of the vertex $C$ is the line :
  35. If a line intercepted between the coordinate axes is trisected at a point $A(4,3)$, which is nearer to the $x$-axis, then its equation is :
  36. Let $A(h,k)$, $B(1,1)$ and $C(2,1)$ be the vertices of a right angled triangle with $AC$ as its hypotenuse. If the area of the triangle is $1$ square unit, then the set …
  37. If non zero numbers $a,b,c$ are in H.P., then the straight line $\frac xa+\frac yb+\frac1c=0$ always passes through a fixed point. That point is :
  38. The circumcentre of a triangle lies at the origin and its centroid is the midpoint of the line segment joining the points $\left(a^{2}+1,\ a^{2}+1\right)$ and …
  39. A triangle with vertices $(4,0)$, $(-1,-1)$, $(3,5)$ is :
  40. If the two lines $x+(a-1)y=1$ and $2x+a^{2}y=1$, $(a\in R-\{0,1\})$ are perpendicular, then the distance of their point of intersection from the origin is
  41. Locus of centroid of the triangle whose vertices are $(a\cos t,a\sin t)$, $(b\sin t,-b\cos t)$ and $(1,0)$, where $t$ is a parameter, is :
  42. Locus of mid point of the portion between the axes of $x\cos\alpha+y\sin\alpha=p$ where $p$ is constant is :
  43. The equation of the straight line passing through the point $(4,3)$ and making intercepts on the co-ordinate axes whose sum is $-1$ is :
  44. Given three points $P,Q,R$ with $P(5,3)$ and $R$ lies on the $x$-axis. If the equation of $RQ$ is $x-2y=2$ and $PQ$ is parallel to the $x$-axis, then the centroid of …
  45. If a line $L$ is perpendicular to the line $5x-y=1$, and the area of the triangle formed by the line $L$ and the coordinate axes is $5$ sq units, then the distance of …
  46. A square, of each side $2$, lies above the $x$-axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle $30^\circ$ with the …
  47. If $(a,a^{2})$ falls inside the angle made by the lines $y=\frac x2$, $x>0$ and $y=3x$, $x>0$, then $a$ belong to :
  48. A straight line through the point $A(3,4)$ is such that its intercept between the axes is bisected at $A$. Its equation is :
  49. A square of side $a$ lies above the $x$-axis and has one vertex at the origin. The side passing through the origin makes an angle $\alpha\left(0<\alpha<\frac\pi4\right)$ …
  50. If a vertex of a triangle is $(1,1)$ and the mid points of two sides through this vertex are $(-1,2)$ and $(3,2)$ then the centroid of the triangle is :

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