wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The equations xy=4 and x2+4xy+y2=0 represent the sides of

A
an equilateral triangle
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
a right angled triangle
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
an isosceles triangle
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
a right angled isosceles triangle
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A an equilateral triangle
x2+4xy+y2=0(yx)2+4yx+1=0yx=2±3
Acute angle between the lines is tan1(241)1+1=π3
Now angle made by the line xy=4 and yx=2±3
=tan1∣ ∣2±311+(2±3)∣ ∣=tan1∣ ∣3(3±1)1±3∣ ∣=π3
Hence the lines will form a equilateral triangle

Alternate Solution:
Acute angle between pair of lines x2+4xy+y2=0
=tan122212=π3
the line y=x+c makes equal angle with x2+4xy+y2=0
[y=x doesn't change the pair of lines x2+4xy+y2=0]
all angles of the triangle are equal to 60°
Hence triangle is equilateral triangle

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
A Pair of Straight Lines
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon