Circles

JEE Advanced · Mathematics · 44 past questions

1. Q1 2025 Paper 2

   Let $P(x_1,y_1)$ and $Q(x_2,y_2)$ be two distinct points on the ellipse…

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2. Q2 2024 Paper 1

   Let the straight line $y=2x$ touch a circle with center $(0,\alpha)$, $\alpha>0$, and radius $r$ at a point…

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3. Q3 2023 Paper 2

   Let $A_1, A_2, A_3, \ldots, A_8$ be the vertices of a regular octagon that lie on a circle of radius 2. Let…

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4. Q4 2023 Paper 2

   Let $C_1$ be the circle of radius 1 with center at the origin. Let $C_2$ be the circle of radius $r$ with…

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5. Q5 2023 Paper 2

   PARAGRAPH "I"…

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6. Q6 2023 Paper 2

   PARAGRAPH "I"…

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7. Q7 2022 Paper 1

   Let $ABC$ be the triangle with $AB=1$, $AC=3$ and $\angle BAC=\frac{\pi}{2}$. If a circle of radius $r>0$…

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8. Q8 2022 Paper 2

   Let $G$ be a circle of radius $R > 0$. Let $G_1, G_2, \ldots, G_n$ be $n$ circles of equal radius $r > 0$.…

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9. Q9 2021 Paper 1

   Consider a triangle $\Delta$ whose two sides lie on the x-axis and the line $x + y + 1 = 0$. If the…

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10. Q10 2021 Paper 2

    Consider the region $R = \{(x, y) \in \mathbb{R} \times \mathbb{R} : x \geq 0 \text{ and } y^2 \leq 4 - x\}$.…

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11. Q11 2021 Paper 2

    Consider the region $R = \{(x, y) \in \mathbb{R} \times \mathbb{R} : x \geq 0 \text{ and } y^2 \leq 4 - x\}$.…

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12. Q12 2021 Paper 2

    Paragraph…

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13. Q13 2021 Paper 2

    Paragraph…

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14. Q14 2020 Paper 2

    Let $O$ be the centre of the circle $x^2 + y^2 = r^2$, where $r > \frac{\sqrt{5}}{2}$. Suppose $PQ$ is a…

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15. Q15 2019 Paper 1

    A line $y=mx+1$ intersects the circle $(x-3)^2+(y+2)^2=25$ at the points $P$ and $Q$. If the midpoint of the…

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16. Q16 2019 Paper 1

    Let the point $B$ be the reflection of the point $A(2,3)$ with respect to the line $8x-6y-23=0$. Let…

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17. Q17 2019 Paper 2

    Answer Q.17 and Q.18 by appropriately matching the lists based on the information given in the paragraph.…

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18. Q18 2019 Paper 2

    Answer Q.17 and Q.18 by appropriately matching the lists based on the information given in the paragraph.…

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19. Q19 2018 Paper 1

    PARAGRAPH “X”…

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20. Q20 2018 Paper 1

    PARAGRAPH “X”…

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21. Q21 2018 Paper 2

    Let $T$ be the line passing through the points $P(-2,7)$ and $Q(2,-5)$. Let $F_1$ be the set of all pairs of…

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22. Q22 2017 Paper 1

    For how many values of $p$, the circle $x^2 + y^2 + 2x + 4y - p = 0$ and the coordinate axes have exactly…

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23. Q23 2016 Paper 1

    The circle $C_1: x^2+y^2=3$, with centre at $O$, intersects the parabola $x^2=2y$ at the point $P$ in the…

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24. Q24 2016 Paper 1

    Let $RS$ be the diameter of the circle $x^2+y^2=1$, where $S$ is the point $(1,0)$. Let $P$ be a variable…

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25. Q25 2015 Paper 1

    If the normals of the parabola $y^2=4x$ drawn at the end points of its latus rectum are tangents to the…

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26. Q26 2014 Paper 1

    A circle $S$ passes through the point $(0,1)$ and is orthogonal to the circles $(x-1)^2+y^2=16$ and…

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27. Q27 2014 Paper 2

    The common tangents to the circle $x^2+y^2=2$ and the parabola $y^2=8x$ touch the circle at the points $P, Q$…

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28. Q28 2013 Paper 2

    Circle(s) touching $x$-axis at a distance 3 from the origin and having an intercept of length $2\sqrt{7}$ on…

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29. Q29 2012 Paper 1

    The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line…

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30. Q30 2012 Paper 1

    Let $S$ be the focus of the parabola $y^2=8x$ and let $PQ$ be the common chord of the circle…

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31. Q31 2012 Paper 2

    Paragraph for Questions 53 and 54…

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32. Q32 2012 Paper 2

    Paragraph for Questions 53 and 54…

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33. Q33 2011 Paper 2

    The circle passing through the point $(-1,0)$ and touching the $y$-axis at $(0,2)$ also passes through the…

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34. Q34 2011 Paper 2

    The straight line $2x-3y=1$ divides the circular region $x^2+y^2\le6$ into two parts. If…

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35. Q35 2010 Paper 2

    Two parallel chords of a circle of radius $2$ are at a distance $\sqrt{3}+1$ apart. If the chords subtend at…

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36. Q36 2009 Paper 1

    Tangents drawn from the point $P(1,8)$ to the circle…

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37. Q37 2009 Paper 2

    The centres of two circles $C_1$ and $C_2$ each of unit radius are at a distance of 6 units from each other.…

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38. Q38 2008 Paper 1

    A straight line through the vertex $P$ of a triangle $PQR$ intersects the side $QR$ at the point $S$ and the…

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39. Q39 2008 Paper 1

    Paragraph for Question Nos. 15 to 17…

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40. Q40 2008 Paper 1

    Paragraph for Question Nos. 15 to 17…

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41. Q41 2008 Paper 1

    Paragraph for Question Nos. 15 to 17…

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42. Q42 2008 Paper 2

    Consider…

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43. Q43 2007 Paper 1

    Tangents are drawn from the point $(17, 7)$ to the circle $x^2 + y^2 = 169$.…

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44. Q44 2007 Paper 2

    Match the statements in Column I with the properties in Column II and indicate your answer by darkening the…

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