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Mathematics Test 11 - Straight Line, Circle


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30 Questions MCQ Test JEE Main & Advanced Mock Test Series | Mathematics Test 11 - Straight Line, Circle

Mathematics Test 11 - Straight Line, Circle for JEE 2022 is part of JEE Main & Advanced Mock Test Series preparation. The Mathematics Test 11 - Straight Line, Circle questions and answers have been prepared according to the JEE exam syllabus.The Mathematics Test 11 - Straight Line, Circle MCQs are made for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Mathematics Test 11 - Straight Line, Circle below.
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Mathematics Test 11 - Straight Line, Circle - Question 1

A point P on y-axis is equidistant from the points A(–5,4) and B(3,–2). Its co-ordinates are

Mathematics Test 11 - Straight Line, Circle - Question 2

If the point P(x,y) be equidistant from the points A(a b, b–a) and B(a–b,a b), then

Detailed Solution for Mathematics Test 11 - Straight Line, Circle - Question 2
PA=PB
take square both side 
PA^2=PB^2

now use distance
formula ,
{x-(a+b)}^2+{y-(b-a)}^2={x-(a-b)}^2+{y-(a+b)}^2

=>x^2+(a+b)^2-2x(a+b)+y^2+(b-a)^2-2y(b-a)y=x^2+(a-b)^2-2x(a-b)+y^2+(a+b)^2-2y(a+b)

=>2x(a-b)-2x(a+b)=2y(b-a)-2y(a+b)

=>2x{a-b-a-b}=2y{b-a-a-b}

=>2x(-2b)=2y(-2a)

=>bx=ay 
Mathematics Test 11 - Straight Line, Circle - Question 3

The points (0,8/3),(1,3) and (82,30) are the vertices of

Mathematics Test 11 - Straight Line, Circle - Question 4

P(3,1),Q(6,5) and R(x,y) are three points such that the angle PRQ is a right angle and the area of
RPQ= 7, then the number of such point R is

Mathematics Test 11 - Straight Line, Circle - Question 5

Determine the ratio in which the line 3x + 4y - 9 = 0 divides the line segment joining the points (1,3) and (2,7).

Mathematics Test 11 - Straight Line, Circle - Question 6
Given four lines with equations x+2y–3 = 0, 3x+4y–7 = 0, 2x+3y–4 = 0, 4x+5y–6 = 0, then
Mathematics Test 11 - Straight Line, Circle - Question 7

......PS be the median of the triangle with vertices P(2,2), Q(6,–1) and R(7,3). The equation of the line passing through (1,–1) and parallel to PS is

Mathematics Test 11 - Straight Line, Circle - Question 8
The line 4x+y = cuts the axis of co-ordinates at A and B. If C is the foot of perpendicular drawn from origin O, then AC : CB =
Mathematics Test 11 - Straight Line, Circle - Question 9
Points on the line x+y = 4 that lie at a unit distance from the line 4x+3y–10 = 0 are
Mathematics Test 11 - Straight Line, Circle - Question 10
A line passes through (2,2) and is perpendicular to the line 3x+y = 3. Its y intercept is
Mathematics Test 11 - Straight Line, Circle - Question 11
The four lines axby c=0 enclose a
Mathematics Test 11 - Straight Line, Circle - Question 12
The reflection of the point(4,–13) in the line 5x+y+6= 0 is
Mathematics Test 11 - Straight Line, Circle - Question 13
The equation of the bisector of the acute angle between the lines 3x–4y+7 = 0 and 12x+5y–2 = 0 is
Mathematics Test 11 - Straight Line, Circle - Question 14
The vertices of a triangle ABC are (1,1), (4,–2) and (5,5) respectively. Then equation of perpendicular dropped from C to the internal bisector of angle A is
Mathematics Test 11 - Straight Line, Circle - Question 15
A line is such that its segements between the straight lines 5x–y = 4 and 3x+4y–4 = 0 is bisected at the point (1,5). Its equation is
Mathematics Test 11 - Straight Line, Circle - Question 16

The radius of the circle whose centre is on y-axis and which passes through the points (5,2) and (7,–4) is

Mathematics Test 11 - Straight Line, Circle - Question 17
Two circles and 0 are such that they
Detailed Solution for Mathematics Test 11 - Straight Line, Circle - Question 17 These are the equation of two circles.The best way to find out whether two circles touches or cuts or do not intersect is to find out the distance between their centres.If this distance is greater than the sum of their radii they don't touch,if equal to sum of radii they just touch, and if less than sum of radii then intersect at two points. If distance is zero then they are concentric.
Mathematics Test 11 - Straight Line, Circle - Question 18
3x+4y–7 = 0 is common tangent at (1,1) to two equal circles of radius 5. Their centres are the points
Mathematics Test 11 - Straight Line, Circle - Question 19

The points (2,3),(0,2),(4,5)and (0,c) are concyclic if the value of c is

Mathematics Test 11 - Straight Line, Circle - Question 20
Equation of the diameter of the circle  which passes through the origin is
Mathematics Test 11 - Straight Line, Circle - Question 21
Which of the following lines is a normal to the circle
Mathematics Test 11 - Straight Line, Circle - Question 22
The equation represents
Mathematics Test 11 - Straight Line, Circle - Question 23

The coordinates of the point on the circle x2+y2-12x-4y+30=0 which is the farthest from the origin are

Detailed Solution for Mathematics Test 11 - Straight Line, Circle - Question 23
Centre of the given circle is - (-12/2) , - ( -4/2)
This means (6,2) is the centre of the circle. 
The farthest point from the origin on the circle has to be the far end of diameter got by joining (0,0) and (6,2)
Equation of line joining these two points is by two point formula
We have x = 3 y 
The point of intersection of this line and circle is got by solving these two
We get points (3,1) and (9,3)
Hence required farthest is (9,3)
Mathematics Test 11 - Straight Line, Circle - Question 24
The angle between two tangents from the origin to the circle is
Mathematics Test 11 - Straight Line, Circle - Question 25
The number of tangents that can be drawn from the point (8,6) to the circle is
Mathematics Test 11 - Straight Line, Circle - Question 26
The equation of the common tangent to the circle , at their point of contact is
Mathematics Test 11 - Straight Line, Circle - Question 27
The intercepts made by the circle on the x-axis and y-axis are respectively
Mathematics Test 11 - Straight Line, Circle - Question 28
The circle touches x-axis, then c =
Mathematics Test 11 - Straight Line, Circle - Question 29
The equation of the passing through the intersection of the circles and having its centre on the line y = x is
Mathematics Test 11 - Straight Line, Circle - Question 30

The vertex A of a triangle ABC is the point (-2, 3) whereas the line perpendicular to the sides AB and AC are x – y – 4 = 0 and 2x – y – 5 = 0 respectively. The right bisectors of sides meet at P(3/2 , 5/2) . Then the equation of the median of side BC is

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