Test: Circles - 5 - JEE MCQ

# Test: Circles - 5 - JEE MCQ

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## 25 Questions MCQ Test - Test: Circles - 5

Test: Circles - 5 for JEE 2024 is part of JEE preparation. The Test: Circles - 5 questions and answers have been prepared according to the JEE exam syllabus.The Test: Circles - 5 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Circles - 5 below.
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Test: Circles - 5 - Question 1

### The equation of the circle which touches the axis of y at the origin and passes through (3, 4) is

Detailed Solution for Test: Circles - 5 - Question 1

Test: Circles - 5 - Question 2

### The equation to the circle whose radius is 4 and which touches the negative x-axis at a distance 3 units from the origin is

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Test: Circles - 5 - Question 3

### Number of different circles that can be drawn touching 3 lines, no two of which are parallel and they are neither coincident nor concurrent, are

Detailed Solution for Test: Circles - 5 - Question 3

If three lines are given such that no two of them are parallel and they are not concurrent then a definite triangle is formed by them. There are four circles which touch sides of a triangle (3-excircles and 1-incircle).

Test: Circles - 5 - Question 4

If a circle of constant radius 3k passes through the origin `O' and meets co-ordinate axes at A and B then the locus of the centroid of the triangle OAB is

Detailed Solution for Test: Circles - 5 - Question 4

let centroid of circle is (l,m)
then point A and B will be as shown in figure
and center of circle will be (3l/2 ,3m/2)
so (3k)2 =(3l/2)2 +(3m/2)2
(2k)2 =(l)2 +(m)2
so locus
x2 +y2 = (4k)2
x2 + y2 = (2k)2

Test: Circles - 5 - Question 5

A pair of tangents are drawn from the origin to the circle x2 + y2 + 20(x + y) + 20 = 0. The equation of the pair of tangents is

Detailed Solution for Test: Circles - 5 - Question 5

Given equation of circle is

Test: Circles - 5 - Question 6

The locus of the centre of a circle which touches externally the circle, x2 + y2 – 6x – 6y + 14 = 0 and also touches the y-axis is given by the equation

Detailed Solution for Test: Circles - 5 - Question 6

let the center of the circle be (h,k) and since it touches the y-axis
Therefore, its radius will be h it touches the circle x2+y2−6x−6y+14=0 externally
Therefore, C1C2 = r1 + r2
⇒ [(h-3)2 + (k-3)2]½ = h+2
⇒ k2−10h−6k+14=0
⇒ y2−10x−6y+14=0

Test: Circles - 5 - Question 7

The common chord of two intersecting circles C1 and C2 can be seen from their centres at the angles of 90º and 60º respectively. If the distance between their centres is equal to √3 + 1 then the radius of C1 and C2 are

Test: Circles - 5 - Question 8

A circle touches a straight line lx + my + n = 0 and cuts the circle x2 + y2 = 9 orthogonally, The locus of centres of such circles is

Detailed Solution for Test: Circles - 5 - Question 8

Let the equation of the circle is-
x2+y2+2gx+2fy+c = 0
Given, this circle is orthogonal to x2 +y2 −9=0
Condition of orthogonality

Test: Circles - 5 - Question 9

The length of the common chord of circles x2 + y2 – 6x – 16 = 0 and x2 + y2 – 8y – 9 = 0 is

Test: Circles - 5 - Question 10

If the two circles, x2 + y2 + 2g1x + 2f1y = 0 and x2 + y2 + 2g2x + 2f2y = 0 touches each other, then

Test: Circles - 5 - Question 11

If  &  are four distinct points on a circle of radius 4 units then, abcd =

Test: Circles - 5 - Question 12

What is the length of shortest path by which one can go from (–2, 0) to (2, 0) without entering the interior of circle, x2 + y2 = 1

Detailed Solution for Test: Circles - 5 - Question 12

Center of circle = C(0,0), radius, r=1.
Tangents from Point A(−2,0) and B(2,0) meets circle at points P
respectively.

Test: Circles - 5 - Question 13

Three equal circles each of radius r touch one another. The radius of the circle touching all the three given circle internally is

Test: Circles - 5 - Question 14

In a right triangle ABC, right angled at A, on the leg AC as diameter, a semicircle is described. The chord joining A with the point of intersection D of the hypotenuse and the semicircle, then the length AC equals to

Test: Circles - 5 - Question 15

The circle passing through the distinct points (1, t), (t, 1) & (t, t) for all values of `t'. passes through the point

Test: Circles - 5 - Question 16

The locus of the mid points of the chords of the circle x2 + y2 – ax – by = 0 which subtend a right angle at  is

Test: Circles - 5 - Question 17

A circle is inscribed into a rhombus ABCD with one angle 60º. The distance from the centre of the circle to the nearest vertex is equal to 1. If P is any point of the circle, then | PA |2 + | PB |2 + | PC |2 + | PD |2 is equal to

Test: Circles - 5 - Question 18

Number of points (x, y) having integral coordinates satisfying the condition x2 + y2 < 25 is

Detailed Solution for Test: Circles - 5 - Question 18

Since x2+y2<25 and a and y are integers, the possible values of x and y∈(0,±1,±2,±3,±4,).
Thus,x and y can be chosen in 9 ways each and (x,y) can be chosen in 9×9=81 ways.
However, we have to exclude cases (±3,±4),(±4,±3)
and (±4,±4)i.e.,3×4=12
Hence, the number of permissible values = 81−12=69

*Multiple options can be correct
Test: Circles - 5 - Question 19

Circles are drawn touching the co-ordinate axis and having radius 2, then

*Multiple options can be correct
Test: Circles - 5 - Question 20

For the circles S1 º x2 + y2 – 4x – 6y – 12 = 0 and S2 º x2 + y2 + 6x + 4y – 12 = 0 and the line L º x + y = 0

*Multiple options can be correct
Test: Circles - 5 - Question 21

x2 + y2 + 6x = 0 and x2 + y2 - 2x = 0 are two circles, then

*Multiple options can be correct
Test: Circles - 5 - Question 22

3 circle of radii 1, 2 and 3 and centres at A, B and C respectively, touch each other. Another circle whose centre is P touches all these 3 circles externally. and has radius r. Also ∠PAB = q & ∠PAC = a.

*Multiple options can be correct
Test: Circles - 5 - Question 23

Slope of tangent to the circle (x – r)2 + y2 = r2 at the point (x, y) lying on the circle is

Detailed Solution for Test: Circles - 5 - Question 23

Given equation ⟶(x−r)2+y2 = r2
Tangent to this, dy/dx​=0
⟹ 2(x−r)+2ydy/dx=0
dy/dx = (r−x)/y

*Multiple options can be correct
Test: Circles - 5 - Question 24

The centre(s) of the circle(s) passing through the points (0, 0), (1, 0) and touching the circle x2 + y2 = 9 is/are

*Multiple options can be correct
Test: Circles - 5 - Question 25

Point M moved along the circle (x – 4)2 + (y – 8)2 = 20. Then it broke away from it and moving along a tangent to the circle cuts the x-axis at the point (–2, 0). The co-ordinates of the point on the circle at which the moving point broke away can be

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