Question

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

Solution

Correct option is

an equilateral triangle

 

Acute angle between the lines x2 + 4xy + y2 = 0 is  

                        

Angle bisectors of x2 + 4xy + y2 = 0 are given by

              

  

As x + y = 0 is perpendicular to x – = 4, the given triangle is isosceles with vertical angle equal to π/3 and hence it is equilateral. 

SIMILAR QUESTIONS

Q1

The line x + y = a, meets the axis of x and y at A and B respectively. A triangle AMN is inscribed in the triangle OABO being the origin, with right angle at NM and N lie respectively on OB and AB. If the area of the triangle AMN is 3/8 of the area of the triangle OAB, then AN/BN is equal to.

Q2

The point (4, 1) undergoes the following transformation successively.

(i) Reflection about the line y = x

(ii) Translation through a distance 2 units along the positive direction of x-axis.

(iii) Rotation through an anlge π/4 about the origin in the anticlockwise direction  

(iv) Reflection about x = 0

The final position of the given point is

 

Q3

A line cuts the x-axis at (7, 0) and the y-axis at B(0, –5). A variable linePQ is draw perpendicular to AB cutting the x-axis at P and the y-axis at in θ. If AQ and BP intersect at R, the locus of R is

Q4

Equation of a line which is parallel to the line common to the pair of lines given by 6x2 – xy – 12y2 = 0 and 15x2 + 14xy – 8y2 = 0 and the sum of whose intercepts on the axes is 7, is 

Q5

If pairs of lines x2 + 2xy + ay2 = 0 and ax2 + 2xy + y2 = 0 have exactly one line in common then the joint equation of the other two lines is given by 

Q6

If the lines joining the origin to the intersection of the line y = mx + 2 and the curve x2 + y2 = 1 are at right angles, then 

Q7

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  

Q8

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 

Q9

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 

Q10

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