Straight Lines-Quiz-8

Straight Lines Quiz-8

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. The area of the triangle formed by the lines y=ax,x+y-a=0 and the y-axis is equal to

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Solution

Q2. The coordinates of the foot of the perpendicular from the point (2, 3) on the line -y+3x+4=0 are given by

•  (37/10,-1/10)
•  (-1/10,37/10)
•  (10/37,-10)
•  (2/3,-1/3)

Solution

Q3. Let PS be the median of the triangle with vertices P(2,2),Q(6,-1) and R(7,3). The equation of the line passing through (1,-1) and parallel to PS is

•  2x-9y-7=0
•  2x-9y-11=0
•  2x+9y-11=0
•  2x+9y+7=0

Solution

Q4. The pair of lines represented by 3ax²+5xy+(a²-2) y²=0 are perpendicular to each other for

•  Two values of a
•  a
•  For one value of a
•  For no value of a

Solution

Q5. The line L₁=4x+3y-12=0 intersects the x-and the y-axes at A andB, respecetively. A variable line perpendicular to L₁ intersects the x-and the y-axes at P and Q, respectively. Then the locus of the circumcentre of triangle ABQ is

•  3x-4y+2=0
•  4x+3yy+7=0
•  6x-8y+7=0
•  None of these

Solution

Q6. Two sides of a triangle are along the coordinate axes and the medians through the vertices (other than the origin) are mutually perpendicular. the number of such triangles is/are

•  Zero
•  Two
•  Four
•  Infinite

Solution

Q7. The straight lines x+y=0,3x+y-4=0,x+3y-4=0 from a triangle which is

•  Isosceles
•  Equilateral
•  Right angle
•  None of these

Solution

Q8. Let A=(3,-4),B=(1,2), let P=(2k-1,2k+1) be a variable point such that PA+PB is the minimum. then k is

•  7/9
•  0
•  7/8
•  None of these

Solution

Q9. A≡(-4,0),B≡(4,0). M and N are the variable points of y-axis such that M lies below N and MN=4. Line joining AM and BN intersect at 'P'. Locus of 'P' is

•  2xy-16-x²=0
•  2xy+16-x²=0
•  2xy+16+x²=0
•  2xy-16+x²=0

Solution

Q10. The angle between the pair of lines whose equation is 4x²+10xy+my²+5x+10y=0 is

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•  None of these

Solution