(2,3) is a point on the side AB of △ABC. The third vertex C moves such that the sides AC,BC are bisected by x2−y2=0 at right angles. Then C lies on
A
2x−3y=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
3x−2y=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2x+3y=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
3x+2y=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A2x−3y=0 x2−y2=0 ⇒(x−y)(x+y)=0 ⇒x−y=0,x+y=0
Let C≡(h,k)
Then A,B are the images of C in x−y=0,x+y=0 ∴A≡(k,h),B≡(−k,−h)
Slope of AB is hk=h−3k−2 ⇒2h−3k=0