Question

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

Solution

Correct option is

Isosceles, Obtuse-angled

Let the given lines be represented by ABBC and CA, respectively, thenA(–2, 2), B(2, –2) and C(1, 1) are the vertices of a triangle ABC. Also, note that

 This shows that ΔABC is isosceles; it is clearly not right-angled or equilateral. Since

                     

⇒ Δ ABC is obtuse-angled.  

SIMILAR QUESTIONS

Q1

If θ is an angle between the lines given by the equation 6x2 + 5xy – 4y2 + 7x + 13y – 3 = 0, then equation of the line passing through the point of intersection of these lines and making an angle θ with the positive x-axis is 

Q2

If one of the lines given by the equation 2x2 + axy + 3y2 = 0 coincide with one of those given by 2x2 + bxy – 3y2 = 0 and the other lines represented by them be perpendicular, then 

Q3

The equation x – y = 4 and x2 + 4xy + y2 = 0 represent the sides of  

Q4

If the equation of the pair of straight lines passing through the point (1, 1), one making an angle θ with the positive direction of x-axis and the other making the same angle with the positive direction of y-axis is x2 – (a + 2)xy + y2 + a(x + y – 1) = 0,  

a ≠ –2, then the value of sin 2θ is 

Q5

If θ1 and θ2 be the angles which the lines (x2 + y2) (cos2 θ sin2α + sin2 θ) = (x tan α – y sin θ)2 make with axis ofx, then if θ = π/6,

tan θ1 + tan θ2 is equal to  

Q6

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 

Q7

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

Q8

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     

 

Q9

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

Q10

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