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

The circumcentre of the triangle formed by the lines y=2x, y=x and y=3x+4 is


A

(6,8)

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

(6,8)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

(3,4)

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

(-3,4)

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B

(6,8)


Explanation for the correct option:

Step 1: Equating circumradius to find the relation between x,y

The triangle is formed by lines y=x, y=2x and y=3x+4.

Therefore, the coordinates of the triangle are A(0,0),B(-4,-8) and C(-2,-2).

Let the circumcentre of the triangle be P(x,y).

Then, PA2=PB2

x2+y2=(x+4)2+(y+8)2x2+y2=x2+8x+16+y2+64+16y8x+16y+80=0x+2y+10=01

Step 2: Equate circumradius (PA)2=PC2

Similarly

x2+y2=(x+2)2+(y+2)2x2+y2=x2+4x+4+y2+4+4y4x+4y+8=0x+y+2=02

Step 3: Finding the circumcentre

Subtracting equation 1 from equation 2, we get

y=-8.

Substituting the value of y in equation2 we get

x=6

Therefore, the circumcentre of the triangle is (6,-8).

Hence, option (B) is the correct answer.


flag
Suggest Corrections
thumbs-up
6
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Definition and Standard Forms
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon