Question

The straight lines 4x – 3y – 5 = 0, x – 2y – 10 = 0, 7x + 4y – 40 = 0 and x + 3y + 10 = 0 form the sides of a

Solution

Correct option is

Cyclic quadrilateral

Slopes of the lines are 4/3, 1/2, –7 and –1/3, respectively. If α is the angle between first and third. β is the angle between second and fourth.

tan α = –l, tan β = 1 ⇒ α = 135o, β = 45o ⇒ α + β = 180o

so the quadrilateral in cyclic.

Since no two sides are parallel, it can not be a parallelogram or a rectangle.

SIMILAR QUESTIONS

Q1

If two of 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 

Q2

The straight line is x + y = 0, 3x + y – 4 = 0 and x + 3y – 4 = 0 from a triangle which is  

Q3

 If the line x + 2ay + a = 0, x + 3by + b = 0 and x + 4cy + c = 0 are concurrent, then abc are in

Q4

If the line 2 (sin a + sin bx – 2 sin (a – by = 3 and 2 (cos a + cos bx + 2 cos (a – by = 5 are perpendicular, then sin 2a+ sin2b is equal to     

 

Q5

If p1p2 denote the lengths of the perpendiculars from the origin on the lines x sec α + y cosec α = 2a and

x cos α + y sin α = a cos 2α respectively, then  is equal to

Q6

The locus of the point of intersection of the lines x sin θ + (1 – cos θ) y = a sin θ and x sin θ – (1 + cos θ) y + a sin θ = 0 is

Q7

If two vertices of a triangle are (5, –1) and (–2, 3), and the orthocenter lies at the origin, the coordinate of the third vertex are 

Q8

 

Equation of a line passing through the intersection of the lines

x + 2y – 10 = 0 and 2x + y + 5 = 0 is 

Q9

 The lengths of the perpendicular from the points (m2, 2m), (mmm +m) and (m2, 2m) to the line x + y + 1 = 0 form

Q10

The sine of the angle between the pair of lines represented by the equation x2 – 7xy + 12y2 = 0 is