## Straight Lines Quiz-13

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. If P=(1,0),Q=(-1,0) and R=(2,0) are three given points, then locus of the point S satisfying the relation SQ2+SR2=2SP2 is
•  A straight line parallel to x-axis
•  A circle passing through the origin
•  A circle with the centre at the origin
•  A straight line parallel to y-axis
Solution
Q2. If the equation of the locus of a point equidistant from the points (a1,b1) and (a2,b2) is (a1-a2 )x+(b1-b2 )y+c=0, then the value of c is
•
•
•
•
Solution
Q3. A rectangle ABCD, where A≡(0,0),B≡(4,0),C≡(4,2),D≡(0,2), undergoes the following transformations successively: (i) f1 (x,y)→(y,x), (ii) f2 (x,y)→(x+3y,y), (iii) f3 (x,y)→((x-y)/2,(x+y)/2). The final figure will be
•  A square
•  A rhombus
•  A rectangle
•  A parallelogram
Solution

Q4. The extremities of the base of an isosceles triangle are (2, 0) and (0, 2). If the equation of one of the equal side is x=2, then equation of other equal side is
•  x+y=2
•  x-y+2=0
•  y=2
•  2x+y=2
Solution
Q5. Distance of origin from line (1+√3)y+(1-√3)x=10 along the line y=√3 x+k is
•  5/√2
•  5√2+k
•  10
•  0
Solution
Q6. A light ray coming along the line 3x+4y=5 gets reflected from the line ax+by=1 and goes along the line 5x-12y=10. Then
•  a=64/115,b=112/15
•  a=14/15,b=-8/115
•  a=64/115,b=-8/115
•  a=64/15,b=14/15
Solution

Q7. In a triangle ABC, if A is (2,-1), and 7x-10y+1=0 and 3x-2y+5=0 are equations of an altitude and an angle bisector, respectively, drawn from B, then equation of BC is
•  x+y+1=0
•  5x+y+17=0
•  4x+9y+30=0
•  x-5y-7=0
Solution

Q8. One of the diagonals of a square is the portion of the line x/2+y/3=0 intercepted between the axes. Then the extermities of the other diagonal are
•  (5,5),(-1,1)
•  (0, 0), (4, 6)
•  (0,0),(-1,1)
•  (5, 5), (4, 6)
Solution
Q9. If the extremities of the base of an isosceles triangle are the points (2a,0) and (0,a) and the equation of one of the sides is x=2a, then the area of the triangle is
•  5a2 sq. units
•  5a2/2 sq. units
•  25a2/2 sq. units
•  None of these
Solution
Q10. In a triangle ABC if A≡(1,2) and internal angle bisectors through B and C are y=x and y=-2x, then the inradius r of the ∆ABC is
•  1/√3
•  1/√2
•  2/3
•  None of these
Solution

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