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

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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

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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

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. 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

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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)

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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

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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

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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)

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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

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"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

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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

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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)

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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

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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

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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)  

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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)

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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

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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

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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)

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

A.  θ

B.  2θ

C.  α

D.  2α

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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)

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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

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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

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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

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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

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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

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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

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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)

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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

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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

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