Q66.Let P and Q be two distinct points on a circle which has center at C(2, 3) and which passes through origin O. If OC is perpendicular to both the line segments CP and CQ, then the set {P, Q} is equal to 3 + (1) {(4, 0), (0, 6)} (2) {(2 + 2√2, 3 −√5), (2 −2√2, √5)} + 2√2, 3 + −2√2, 3 (3) {(2 √5), (2 −√5)} (4) {(−1, 5), (5, 1)}
What This Question Tests
The question tests the understanding of circle properties, specifically finding points on a circle such that the line segments from the center to these points are perpendicular to the line joining the center and the origin.
Concepts Tested
Formulas Used
Equation of circle (x-h)² + (y-k)² = r²
Vector dot product for perpendicularity
Parametric coordinates of a circle
📚 NCERT Sections This Tests
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
5.11 — Draw All The Isomers (Geometrical And Optical) Of:
Chemistry Class 11 · Chapter 5
5.11 Draw all the isomers (geometrical and optical) of: (i) [CoCl2(en)2] + (ii) [Co(NH3)Cl(en)2] 2+ (iii) [Co(NH3)2Cl2(en)]+
5.19 — [Cr(Nh3)6] 3+ Is Paramagnetic While [Ni(Cn)4] 2– Is Diamagnetic. Explain Why?
Chemistry Class 11 · Chapter 5
5.19 [Cr(NH3)6] 3+ is paramagnetic while [Ni(CN)4] 2– is diamagnetic. Explain why? 5.20 A solution of [Ni(H2O)6] 2+ is green but a solution of [Ni(CN)4] 2– is colourless. Explain. 5.21 [Fe(CN)6] 4– and [Fe(H2O)6] 2+ are of different colours in dilute solutions. Why?
📋 Question Details
- Chapter
- Circles
- Topic
- Geometric properties of circles
- Year
- 2021
- Shift
- 27 Jul Shift 1
- Q Number
- Q66
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
More from this Chapter
Q94.Consider a family of circles which are passing through the point (−1, 1) and are tangent to x− axis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval (1) 0 < k < 1/2 (2) k ≥1/2 (3) −1/2 ≤k ≤1/2 (4) k ≤1/2
Q79.The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y −3 = 0 is (1) (3, −4) (2) (−3, 4) (3) (−3, −4) (4) (3, 4)
Q67.Three distinct points A, B and C are given in the 2 - dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point (−1, 0) is equal to 31 . Then the circumcentre of the triangle ABC is at the point JEE Main 2009 JEE Main Previous Year Paper (1) (0, 0) (2) ( 54 , 0) (3) ( 25 , 0) (4) ( 53 , 0)
Q68.If P and Q are the points of intersection of the circles x2 + y2 + 3x + 7y + 2p −5 = 0 and x2 + y2 + 2x + 2y −p2 = 0, then there is a circle passing through P, Q and (1, 1) for (1) all values of p (2) all except one value of p (3) all except two values of p (4) exactly one value of p