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QUESTION: 1

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

Solution:

QUESTION: 2

Solution:

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

QUESTION: 3

Solution:

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

Solution:

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).

Solution:

QUESTION: 6

Given four lines with equations x+2y–3 = 0, 3x+4y–7 = 0, 2x+3y–4 = 0, 4x+5y–6 = 0, then

Solution:

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

Solution:

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 =

Solution:

QUESTION: 9

Points on the line x+y = 4 that lie at a unit distance from the line 4x+3y–10 = 0 are

Solution:

QUESTION: 10

A line passes through (2,2) and is perpendicular to the line 3x+y = 3. Its y intercept is

Solution:

QUESTION: 11

The four lines axby c=0 enclose a

Solution:

QUESTION: 12

The reflection of the point(4,–13) in the line 5x+y+6= 0 is

Solution:

QUESTION: 13

The equation of the bisector of the acute angle between the lines 3x–4y+7 = 0 and 12x+5y–2 = 0 is

Solution:

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

Solution:

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

Solution:

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

Solution:

QUESTION: 17

Two circles and 0 are such that they

Solution:
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.

QUESTION: 18

3x+4y–7 = 0 is common tangent at (1,1) to two equal circles of radius 5. Their centres are the points

Solution:

QUESTION: 19

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

Solution:

QUESTION: 20

Equation of the diameter of the circle which passes through the origin is

Solution:

QUESTION: 21

Which of the following lines is a normal to the circle

Solution:

QUESTION: 22

The equation represents

Solution:

QUESTION: 23

The coordinates of the point on the circle x^{2}+y^{2}-12x-4y+30=0 which is the farthest from the origin are

Solution:

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)

QUESTION: 24

The angle between two tangents from the origin to the circle is

Solution:

QUESTION: 25

The number of tangents that can be drawn from the point (8,6) to the circle is

Solution:

QUESTION: 26

The equation of the common tangent to the circle , at their point of contact is

Solution:

QUESTION: 27

The intercepts made by the circle on the x-axis and y-axis are respectively

Solution:

QUESTION: 28

The circle touches x-axis, then c =

Solution:

QUESTION: 29

The equation of the passing through the intersection of the circles and having its centre on the line y = x is

Solution:

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

Solution:

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