Circles · JEE Main previous year questions

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2023 30 questions

Q112023 · 25 Jan 2023 · Shift 1
The points of intersection of the line $a x + b y = 0$ , $(a \neq = b)$ and the circle $x^{2} + y^{2} - 2 x = 0$ are $A (α, 0)$ and $B (1, β)$ . The image of the circle with AB as a diameter in the line $x + y + 2 = 0$ is :
1. A. $x^{2} + y^{2} + 5 x + 5 y + 12 = 0$
2. B. $x^{2} + y^{2} + 3 x + 5 y + 8 = 0$
3. C. $x^{2} + y^{2} - 5 x - 5 y + 12 = 0$
4. D. $x^{2} + y^{2} + 3 x + 3 y + 4 = 0$
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Answer: A
Q102023 · 25 Jan 2023 · Shift 2
Let $z$ be a complex number such that $\frac{z - 2 i}{z + i} = 2, z \neq = - i$ . Then $z$ lies on the circle of radius 2 and centre :
1. A.(0, $- 2$ )
2. B.(0, 0)
3. C.(0, 2)
4. D.(2, 0)
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Answer: A
Q302023 · 25 Jan 2023 · Shift 2· Numerical answer
Points P $(- 3, 2)$ , Q(9, 10) and R $(α, 4)$ lie on a circle C and PR as its diameter. The tangents to C at the points Q and R intersect at the point S. If S lies on the line $2 x - k y = 1$ , then k is equal to ____.
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Answer: 3
Q242023 · 24 Jan 2023 · Shift 1· Numerical answer
Let C be the largest circle centred at $(2, 0)$ and inscribed in the ellipse $\frac{x ^{2}}{36} + \frac{y ^{2}}{16} = 1$ . If $(1, α)$ lies on C, then $10 α^{2}$ is equal to ____
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Answer: 118
Q72023 · 24 Jan 2023 · Shift 2
The locus of the mid points of the chords of the circle $C_{1} : (x - 4)^{2} + (y - 5)^{2} = 4$ which subtend an angle $θ_{i}$ at the centre of the circle $C_{1}$ , is a circle of radius $r_{i}$ . If $θ_{1} = \frac{π}{3}, θ_{3} = \frac{2 π}{3}$ and $r_{1}^{2} = r_{2}^{2} + r_{3}^{2}$ , then $θ_{2}$ is equal to :
1. A. $\frac{π}{2}$
2. B. $\frac{π}{4}$
3. C. $\frac{3 π}{4}$
4. D. $\frac{π}{6}$
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Answer: A