Circle: JEE Main Mathematics Previous Year Questions

164 previous year questions from Circle. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. $The circle on the chord x cos α + y sin α = p of the circle x^{2} + y^{2} = a^{2} as diameter has the equation\dots$
2. $If the point (2, 0), (0, 1), (4, 5) and (0, c) are con-cyclic, then integral value of\dots$
3. $If the circles x^{2} + y^{2} + 5 Kx + 2 y + K = 0 and 2 (x^{2} + y^{2}) + 2 Kx + 3 y - 1 = 0, (K ϵ R), intersect at the points P and Q, then the line\dots$
4. $The two circles x^{2} + y^{2} = ax and x^{2} + y^{2} = c^{2} (c > 0) touch each other if:$
5. $If the points of intersection of the ellipses x^{2} + 2 y^{2} - 6 x - 12 y + 23 = 0 and 4 x^{2} + 2 y^{2} - 20 x - 12 y + 35 = 0 lie on a circle of radius r and centre\dots$
6. $The two points A and B in a plane are such that for all points P lies on circle satisfied \frac{PA}{PB} = k, then k will not be equal to (Ans l\dots$
7. $Let C : x^{2} + y^{2} = 4 and C^{’} : x^{2} + y^{2} - 4 λx + 9 = 0 be two circles. If the set of all values of λ so that the circles\dots$
8. $Let the circle x^{2} + y^{2} = 4 intersect x -axis at the points A (a, 0), a > 0 and B (b, 0) . Let\dots$
9. $Let the lengths of intercepts on X -axis and y -axis made by the circle x^{2} + y^{2} + ax + 2 ay + c = 0 (a < 0) be 22 and\dots$
10. $If a tangent to the circle x^{2} + y^{2} = 1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is:$
11. $Let PQ be a diameter of the circle x^{2} + y^{2} = 9 . If α and β are the lengths of the perpendiculars from P and Q on the straight line\dots$
12. $If the line x - 2 y = m (m \in Z) intersects the circle x^{2} + y^{2} = 2 x + 4 y at two distinct points, then the number of possible values of m are$
13. $If the circles x^{2} + y^{2} - 16 x - 20 y + 164 = r^{2} and (x - 4)^{2} + (y - 7)^{2} = 36 intersect at two distinct points, then:$
14. $The equation of the circle passing through the point (1, 0) and (0, 1) and having the smallest radius is -$
15. $The equation(s) of the common tangent(s) to the circle x^{2} + y^{2} - 6 x = 0 and the parabola, y^{2} = 4 x is:$
16. $The number of common tangents to the circles x^{2} + y^{2} - 4 x - 6 y - 12 = 0 and x^{2} + y^{2} + 6 x + 18 y + 26 = 0, is$
17. $Let PQ and MN be two straight lines touching the circle x^{2} + y^{2} - 4 x - 6 y - 3 = 0 at the points A and B respectively. Let O be the centre of the circle and\dots$
18. $The tangents are drawn from the point (4, 5) to the circle x^{2} + y^{2} - 4 x - 2 y - 11 = 0 . The area of quadrilateral formed by these tangents and radii, is$
19. $The equation of the circle whose centre lies on the line x - 4 y = 1 and which passes through the points (3, 7) and (5, 5) is$
20. $Choose the correct statement about two circles whose equations are given below: x^{2} + y^{2} - 10 x - 10 y + 41 = 0 x^{2} + y^{2} - 22 x - 10 y + 137 = 0$
21. $The equation of tangents to the circle x^{2} + y^{2} = 4 which are parallel to x + 2 y + 3 = 0 are$
22. $The points of intersection of the line ax + by = 0 (a \neq = b) and the circle x^{2} + y^{2} - 2 x = 0 are A (α, 0) and\dots$
23. $If y = 2 x is a chord of the circle x^{2} + y^{2} - 10 x = 0, then the equation of the circle of which this chord is a diameter, is\dots$
24. $If the straight line a x + b y = 2; a, b \neq = 0 touches the circle x^{2} + y^{2} - 2 x = 3 and is normal to the circle x^{2} + y^{2} - 4 y = 6 then the value of\dots$
25. $Let the set of all values of r, for which the circles (x + 1)^{2} + (y + 4)^{2} = r^{2} and x^{2} + y^{2} - 4 x - 2 y - 4 = 0 intersect at two\dots$

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Circle: JEE Main Mathematics Previous Year Questions

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