Straight Lines-Quiz-9

Straight Lines Quiz-9

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 two the lines represented by x⁴+x³ y+cx² y²-xy³+y⁴=0 bisect the angle between the other two, then the value of c is

•  0
•  -1
•  1
•  -6

Solution

Q2. The locus of the orthocentre of the triangle formed by the lines (1+p)x-py+p(1+p)=0,(1+q)x-qy+q(1+q)=0 and y=0, where p≠q is

•  A hyperbola
•  A parabola
•  An ellipse
•  A straight line

Solution

Q3. The straight lines 7x-2y+10=0 and 7x+2y-10=0 form an isosceles triangle with the line y=2. area of this triangle is equal to

•  15/7 sq. units
•  10/7 sq. units
•  18/7 sq. units
•  None of these

Solution

Q4. An equation of a line through the point (1, 2) whose distance from the point (3, 1) has the greatest value is

•  y=2x
•  y=x+1
•  x+2y=5
•  y=3x-1

Solution

Q5. The orthocentre of the triangle formed by the lines xy=0 and x+y=1 is

•  (1/2, 1/2)
•  (1/3, 1/3)
•  (0, 0)
•  (1/4, 1/4)

Solution

Q6. The centroid of an equilateral triangle is (0, 0). If two vertices of the triangle lie on x+y=2√2 then one of them will have its coordinates

•  (√2+√6,√2-√6)
•  (√2+√3,√2-√3)
•  (√2+√5,√2-√5)
•  None of these

Solution

Q7. If the equation of base of an equilateral triangle is 2x-y=1 and the vertex is (-1,2), then the length of the sides of the triangle is

•  
•  
•  
•  

Solution

Q8. Let PQR be a right-angled isosceles triangle, right angled at P(2,1). If the equation of the line QR is 2x+y=3, then the equation representing the pair of lines PQ and PR is

•  3x²-3y²+8xy+20x+10y+25=0
•  3x²-3y²+8xy-20x-10y+25=0
•  3x²-3y²+8xy+10x+15y+20=0
•  3x²-3y²-8xy-15y-20=0

Solution

Q9. A line is drawn perpendicular to line y=5x, meeting the coordinate axes at A and B. If the area of triangle OAB is 10 sq. units where 'O' is the origin, then the equation of drawn line is

•  3x-y-9
•  x-5y=10
•  x+4y=10
•  x-4y=10

Solution

Q10. If a/bc=-2=√(b/c)+√(c/b), where a,b,c>0, then family of lines √a x+√b y+√c=0 passes through the fixed point given by

•  (1, 1)
•  (1, -2)
•  (-1, 2)
•  (-1, 1)

Solution