### Eamcet - Maths - Straight Lines

I: The circum centre of the triangle with vertices (1, √3), (1, √2), (3, -√3) is (2, 0). II: The ortho-centre of the triangle formed by the lines 4x-7y+10=0, x+y=5, 7x+4y=15 is (1, 2)

A.  Only I is true

B.  Only II is true

C.  Both I and II are true

D.  Neither I nor II are true

The arrangement of the following straight lines in ascending order of their slopes A) 2y=√3x    B) y=2     C) y=x               D) y=-x

A.  A, B, C, D

B.  D, B, A, C

C.  B, C, D, A

D.  D, A, B, C

The triangle formed by 2x+3y-7=0 and 3(2x+3y)2-(3x-2y)2=0 is

A.  Equilateral

B.  Isosceles

C.  Right angled

D.  Right angled isosceles

. I: The equation to the pair of lines passing through the point (2,-1) and parallel to the pair of lines 3x2-5xy+2y2-17x+14y+24=0. II: The equation to the pair of lines passing through (1,-1) and perpendicular to the pair of lines x2-xy-2y2=0 is 2x2-xy-y2-5x-y+2=0.

A.  only I is true

B.  only II is true

C.   both I and II are true

D.  neither I nor II are true

The incentre of the triangle formed by (-36,7) , (20,7) and (0,-8) is

A.  (1,0)

B.  (-1,0)

C.  (0,1)

D.  (0,-1)

The condition that the equation ax2+by2+c(x+y)=0 to represents a pair of straight lines is

A.  a+b=0 or c=0

B.  a+b=0 or c+0,ab

C.  ab>0,c=0

D.  none

The area of the triangle formed by(a+3,a-2), (a-4,a+5) and  (a,a) is

A.  0

B.  a

C.  7/2

D.  a2

If the orthocenter of the angle formed by the lines 2x+3y-1=0, x+2y-1=0, ax+by-1=0  is at the origin, then (a, b) is given by

A.  (6, 4)

B.  (-3, 3)

C.  (-8, 8)

D.  (0, 7)

The length of the intercept on the y-axis cut by the pair of lines 2x2+4xy-6y2+3x+y+1=0 is

A.  6/5

B.  5/6

C.  √5/6

D.  √5/3

"The points (0,"  8/3   )," (1, 3), (82, 30) are"

A.  The vertices of obtuse angled triangle

B.  The vertices of acute angled triangle

C.  The vertices of right angled triangle

D.  Collinear

The equation of the line whose x-intercept is 2/5 and which is parallel to 2x-3y+5=0 is

A.  2x-5y+4=0

B.  10x-15y-4=0

C.  28x-21y+12=0

D.  20x+12y+9=0

If (2,4), (4,2) are the extremities of the hypotenuse of a right angled isosceles triangle, then the third vertex is

A.  (2,2) or (4,4)

B.  (3,3) or (4,4)

C.  (2,2) or (3,3)

D.  (2,3) or (3,2)

Let ABC be a triangle. If P is point such that APdivides BC in the ratio 2:3, BP divides CA in the ratio 3:5 then the ratio in which CP divides AB is

A.  2:5

B.  2: -5

C.  5:2

D.  5: -2

The area of the triangle formed by the y-axis, the line L passing through the point (1, 1) and (2, 0) and straight line perpendicular to the line L and passing through (1/2, 0) is

A.  25/19

B.  25/16

C.   23/16

D.  23/19

Circum centre of the ?le formed by the points (2, -5), (2, 7), (4, 7) is

A.  (1,3)

B.  (-2, -3)

C.  (3, 1)

D.  (7, 5)

Two opposite vertices of a square are (1,-2) and (-5,6) then the other two vertices are

A.  (2,5);(-6,-1)

B.  (2,-5); (-6,-1)

C.  (-2,5) ; (6,1)

D.  (2,5) ;(6,1)

The angle between the lines formed by joining the points (2, -3), (-5, 1) and (7, -1), (0, 3) is

A.  π/2

B.  π/4

C.  0

D.  π/6

The vertices of a triangle are (2, 4), (4, -2), (-3, -6).Then the origin lies

A.  inside the triangle

B.  outside the triangle

C.  on one of the sides of the triangle

D.  none

The angles of the triangle formed by the lines 5x+3y-15=0, x+y-4=0, 2x+y-6=0 is

A.  cos-1(4/√17), cos-1(13/√170), π+ cos-1(3/√10)

B.  cos-1(4/√17), cos-1(13/√170), π- cos-1(3/√10)

C.  cos-1(2/√5), π/2,-π/2- cos-1(2/√5)

D.   cos-1(2/√5), π/2,-π/2+cos-1(2/√5)

The angle between the pair of lines (x2+y2)sin2α=(xcosα-ysinα)2 is

A.  θ

B.  2θ

C.  α

D.  2α

The circum centre of the triangle passing through (1, √3), (1, -√3), (3, -√3) is

A.  (2, 0)

B.  (1, 0)

C.  (2, √3)

D.  (0, 2)

The length of the side of the square formed by the lines 2x2+3xy-2y2=0, 2x2+3xy-2y2+3x-5y+1=0 is

A.  1/√3

B.  1/√5

C.  1/√7

D.  1/√10

I: The image of the point (2, 1) with respect to the line x+1=0 is (-4, 1). II: If the point (1, 2) is reflected through origin and then through the line x=y then the new coordinates of the point are (-2, -1)

A.   Only I is true

B.  Only II is true

C.  Both I and II are true

D.   Neither I nor II are true

If the pairs of lines 3x2-5xy+py2=0 and 6x2-xy-5y2=0 have one line in common, then p=

A.  2,25/4

B.  -2,25/4

C.  -2,-25/4

D.  2,-25/4

The equation of  the line having  intercepts a,b on the axes such that a+b =5, ab=6 is

A.  x+y=5

B.  3x+2y-6=0, 2x+3y-6=0

C.  x-3y-3=0,3x-y+3=0

D.  2x+10y-5=0,10x+2y-5=0

Two equal sides of an isosceles triangle are given by equation 7x-y+3=0 and x+y-3=0 and its third side passes through the point (1, 0).The equation of the third side is

A.  3x+y+7=0

B.  x-3y+29=0

C.  3x+y+3=0

D.  3x+y-3=0

If a straight line L is perpendicular to the line 4x-2y=1 and forms a triangle of a area 4 square units with the coordinate axes is

A.  2x+4y+7=0

B.  2x-4y+8=0

C.  2x+4y+8=0

D.  4x-2y-8=0

The extremities of a diagonal of a parallelogram are the points (3, -4) and(-6, 5). If the third vertex is (-2, 1) then the fourth vertex is

A.  (1, 0)

B.  (-1,0)

C.  (1,1)

D.  (-1,-1)

The equations of the diagonal of the square formed by the pairs of lines 12x2+7xy-12y2=0 and 12x2+7xy-12y2-x+7y=1 is

A.  2x-y=1

B.  x-7y=1

C.  7y-x=1

D.  None

A: The orthocentre of the triangle having vertices as (2,3), (2,5), (4,3) is (2,3) R: Orthocentre of a right angled triangle is midpoint of a hypotenuse

A.  A true, R true and R is correct explanation of A

B.  A true, R true but R is not the correct explanation if A

C.  A is true but R is false

D.  A is false but R is true