Q65.If one of the diameters of the circle ๐ฅ2 + ๐ฆ2 - 10๐ฅ+ 4๐ฆ+ 13 = 0 is a chord of another circle ๐ถ, whose center is the point of intersection of the lines 2๐ฅ+ 3๐ฆ= 12 and 3๐ฅ- 2๐ฆ= 5, then the radius of the circle ๐ถ is (1) โ20 (2) 4 (3) 6 (4) 3โ2
What This Question Tests
The problem tests understanding of circle properties, specifically finding the center and radius of a given circle, determining the center of another circle by solving linear equations, and using the relationship between the chord length, radius, and distance from center to chord.
Concepts Tested
Formulas Used
Center of x^2+y^2+2gx+2fy+c=0 is (-g,-f)
Radius of x^2+y^2+2gx+2fy+c=0 is sqrt(g^2+f^2-c)
Distance between two points
Distance from a point to a line (implicitly via chord length)
๐ NCERT Sections This Tests
2.2 โ A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 ยท 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.
2.4 โ A Spherical Conductor Of Radius 12 Cm Has A Charge Of 1.6 ร 10โ7C
Physics Class 11 ยท Chapter 2
2.4 A spherical conductor of radius 12 cm has a charge of 1.6 ร 10โ7C distributed uniformly on its surface. What is the electric field (a) inside the sphere (b) just outside the sphere (c) at a point 18 cm from the centre of the sphere?
5.12 โ Write All The Geometrical Isomers Of [Pt(Nh3)(Br)(Cl)(Py)] And How Many Of
Chemistry Class 11 ยท Chapter 5
5.12 Write all the geometrical isomers of [Pt(NH3)(Br)(Cl)(py)] and how many of these will exhibit optical isomers?
๐ Question Details
- Chapter
- Circles
- Topic
- Equation of Circle
- Year
- 2024
- Shift
- 31 Jan Shift 1
- Q Number
- Q65
- 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 (โ1, 1) and are tangent to xโ 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 โฅ1/2 (3) โ1/2 โคk โค1/2 (4) k โค1/2
Q79.The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y โ3 = 0 is (1) (3, โ4) (2) (โ3, 4) (3) (โ3, โ4) (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 (โ1, 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 โ5 = 0 and x2 + y2 + 2x + 2y โp2 = 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