37. Show that the curves x = y² and xy = k cut orthogonally if 8k2 = 1.
Answers
Answered by
2
Answer:
ANSWER
x=y
2
...(1)
xy=k..(2)
From (1)
(y
2
)y=k⇒y=
3
k
when, y=
3
k
→x=k
3
2
Point of intersection of given curves is (k
3
2
,
3
k
)
x=y
2
1=2y
dx
dy
⇒
dx
dy
=
2y
1
slope of tangent
dx
dy
=
2
3
k
1
...A
xy=k
x
dx
dy
+y=0
dx
dy
=
x
−y
slope of tangent
dx
dy
=
k
3
2
−
3
k
...B
given curves cut at right angle if and only if tangents are perpendicular to each other.
therefore A×B=−1
2
3
k
1
×
k
3
2
−
3
k
=−1
2k
3
2
=1
⇒8k
2
=1
Step-by-step explanation:
plz like and mark me as brainiest
Answered by
0
Answer:
Step-by-step explanation:
Attachments:
Similar questions