Straight Lines-Quiz-13

Straight Lines Quiz-13

Dear Readers,

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