## Straight Lines Quiz-11

The unit Straight Line holds sheer significance in the JEE Advanced and other engineering exams. It has a weightage of 6% pairing with Circles. With focused practice good marks can be fetched from this section. These questions are important in achieving your success in JEE and Other Engineering Exams..

Q1. Given A≡(1,1) and AB is any line through it cutting the x-axis in B. If AC is perpendicular to AB and meets the y-axis in C, then the equation of locus of midpoint P of BC is
•  x+y=1
•  x+y=2
•  x+y=2xy
•  2x+2y=1
Solution
Q2. In a trinagle ABC,A≡(Î±,Î²),B≡(2,3) and C≡(1,3) and point A lies on line y=2x+3 where Î±∈I. Area of ∆ABC,∆, is such that [∆]=5. Possible coordinates of A are (where [.] represents greatest integer function)
•  (2, 3)
•  (5, 13)
•  (-5,-7)
•  (-3,-5)
Solution
Q3. Two vertices of a triangle are (4,-3) and (-2,5). If the orthocentre of the triangle is at (1, 2), then the third vertex is
•  (-33,-26)
•  (33, 26)
•  (26, 33)
•  None of these
Solution

Q4. The line x/3+y/4=1 meets the y-axis and x-axis at A and B, respectively. A square ABCD is constructed on the line segment AB away from the origin. The coordinates of the vertex of the square farthest from the origin are
•  (7, 3)
•  (4, 7)
•  (6, 4)
•  (3, 8)
Solution
Q5. The distance between the two parallel lines is 1 unit. A point 'A' is chosen to lie between the lines at a distance 'd' from one of them. Triangle ABC is equilateral with B on one line and C on the other parallel line. The length of the side of the equilateral triangle is
•
•
•
•
Solution
Q6. The combined equation of straight lines that can be obtained by reflecting the lines y=|x-2| in the y-axis is
•  y2+x2+4x+4=0
•  y2+x2-4x+4=0
•  y2-x2+4x-4=0
•  y2-x2-4x-4=0
Solution

Q7. In ∆ABC the coordinates of the vertex A are (4,-1) and lines x-y-1=0 and 2x-y=3 are internal bisectors of angles B and C. Then, radius of incircle of triangle ABC is
•  4/√5
•  3/√5
•  6/√5
•  7/√5
Solution

Q8. Î¸1 and Î¸2 are the inclination of lines L1 and L2 with x-axis. if L1 and L2 pass through p(x1,y1 ), then equation of one of the angle bisector of these lines is
•
•
•
•
Solution
Q9. OPQR is a square and M,N are the midpoints of the sides PQ and QR, respectively. If the ratio of the areas of the square and the triangle OMN is Î»:6, then Î»/4 is equal to
•  2
•  4
•  2
•  16
Solution
Q10. Consider 3 lines as fallows
L1:5x-y+4=0
L2:3x-y+5=0
L3:x+y+8=0
If these lines enclose a triangle ABC and sum of the squares of the tangent to the interior angles can be expressed in the form p/q where p and q are relatively prime numbers, then the value of p+q is
•  500
•  450
•  230
•  465
Solution

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