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Circle - 2 - JEE MCQ


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30 Questions MCQ Test - Circle - 2

Circle - 2 for JEE 2024 is part of JEE preparation. The Circle - 2 questions and answers have been prepared according to the JEE exam syllabus.The Circle - 2 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Circle - 2 below.
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Circle - 2 - Question 1


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Circle - 2 - Question 2

The radius of  the circle which touches the line  x + y = 0 at M (– 1, 1) and cuts the circle   x2 + y2 + 6x – 4y + 18 = 0  orthogonally, is 

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Circle - 2 - Question 3


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Circle - 2 - Question 4


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Circle - 2 - Question 5


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Circle - 2 - Question 6


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Circle - 2 - Question 7

The angle at which the circles (x – 1)2 + y2 = 10 and  x2 + (y – 2)2 = 5 intersect is

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Circle - 2 - Question 8

Equation of the circle which bisects the circumference of the circle  x2 + y2 + 2 y - 3 = 0 and touches the curve    y = tan (tan–1 x)  at the origin is :

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Circle - 2 - Question 9

Locus of the point of intersection of the pair of perpendicular tangents to the circles x2 + y2 = 1 and x2 + y2 = 7 is the director circle of the circle with radius.

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Circle - 2 - Question 10

Locus of the point of intersection of the pair of perpendicular tangents to the circles x2 + y2 = 1 and x2 + y2 = 7  is the director circle of the circle with radius.

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Circle - 2 - Question 11

Let a and b represent the length of a right triangle's legs. If d is the diameter of a circle inscribed into the triangle, and D is the diameter of a circle superscribed on the triangle, then d + D equals


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Circle - 2 - Question 12

Let a and b represent the length of a right triangle's legs. If d is the diameter of a circle inscribed into the triangle, and D is the diameter of a circle superscribed on the triangle, then d + D equals


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Circle - 2 - Question 13


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Circle - 2 - Question 14


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Circle - 2 - Question 15

The possible radius of a circle whose centre is at the origin and which touches the circle x2 + y2 – 6x – 8y + 21 = 0, is

Detailed Solution for Circle - 2 - Question 15

Let r be the radius of required circle. Now, if two circles touches each other then distance between their centres =|r ± 2| = 5 (given)
∴    r = 3, 7
Note: Equation of circles are x2 + y2 = 9 or x2 + y2 = 49

Circle - 2 - Question 16

The locus of the midpoints of the chords drawn from the point M (1, 8) to the circle  x2 + y2 – 6x – 4y – 11 = 0, is equal to

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Circle - 2 - Question 17


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Circle - 2 - Question 18


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Circle - 2 - Question 19

The  angle  between the two tangents from the origin to the circle  (x - 7)2 + (y + 1)2 = 25 equals

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Circle - 2 - Question 20


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Circle - 2 - Question 21

The radius of  the circle which touches the line  x + y = 0 at M (– 1, 1) and cuts the circle   x2 + y2 + 6x – 4y + 18 = 0  orthogonally, is 

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Circle - 2 - Question 22


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Circle - 2 - Question 23


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Circle - 2 - Question 24


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Circle - 2 - Question 25

A rhombus is  inscribed  in  the  region  common to the two circles  x2 + y2 - 4x - 12 = 0  and x2 + y2 + 4x - 12 = 0  with two of its vertices on the line joining the centres of the circles. The area of  the  rhombous is  :

Detailed Solution for Circle - 2 - Question 25

Circle - 2 - Question 26

The angle at which the circles (x – 1)2 + y2 = 10 and  x2 + (y – 2)2 = 5 intersect is

Detailed Solution for Circle - 2 - Question 26

Circle - 2 - Question 27

Equation of the circle which bisects the circumference of the circle  x2 + y2 + 2 y - 3 = 0 and touches the curve    y = tan (tan–1 x)  at the origin is :

Detailed Solution for Circle - 2 - Question 27


Circle - 2 - Question 28

Let a and b represent the length of a right triangle's legs. If d is the diameter of a circle inscribed into the triangle, and D is the diameter of a circle superscribed on the triangle, then d + D equals



Detailed Solution for Circle - 2 - Question 28

Circle - 2 - Question 29

Locus of the point of intersection of the pair of perpendicular tangents to the circles x2 + y2 = 1 and x2 + y2 = 7  is the director circle of the circle with radius.

Detailed Solution for Circle - 2 - Question 29


Circle - 2 - Question 30

Let a and b represent the length of a right triangle's legs. If d is the diameter of a circle inscribed into the triangle, and D is the diameter of a circle superscribed on the triangle, then d + D equals


Detailed Solution for Circle - 2 - Question 30


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