CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

Straight lines xy=7 and x+4y=2 intersect at B. Points A and C are so chosen on these two lines such that AB=AC. The equation of line AC passing through (2,7) is

A
xy9=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
23x+7y+3=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
2xy11=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
7x6y56=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 23x+7y+3=0
Let the slope of the line AC be m.
Then, the equation of AC be y+7=m(x2).

Slope of the line xy=7 is 1 and slope of the line x+4y=2 is 14.

Let the angle between line AB and BC be θ.
tanθ=∣ ∣ ∣ ∣1(14)1+1(14)∣ ∣ ∣ ∣
tanθ=53

In ABC, AB=AC
ABC=ACB=θ
tan(ABC)=tan(ACB)
53=∣ ∣ ∣ ∣m(14)1+m(14)∣ ∣ ∣ ∣
53=±⎜ ⎜ ⎜m+141m4⎟ ⎟ ⎟

On solving, we get
m=1,237
m1 because if m=1, then we get the line which is parallel to xy=7
So, m=237

Equation of line AC is 23x+7y+3=0

flag
Suggest Corrections
thumbs-up
1
mid-banner-image
mid-banner-image
Join BYJU'S Learning Program
Select...
similar_icon
Related Videos
thumbnail
lock
Tango With Straight Lines !!
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
Select...