find the angle of the intersection of the two following curves x^2=4y, y(x^2+4)=8
Answers
Answer: We can use differential calculus to determine the angle between two curves at ... For more details, see Quora User's answer to How can we determine the ... Originally Answered: What is the angle of intersection of the curves x^2=4y and y^2=4x .
Step-by-step explanation:
Answer:
ANSWER
Given curves are
x
2
+4y
2
=8, ..............(1)
x
2
−2y
2
=2 ...............(2)
2x+8yy
′
=0, 2x−4yy
′
=0
y
′
=−
8y
−2x
y
′
=
4y
2x
(m
1
) (m
2
)
Also, point of intersection,
x
2
=8−4y
2
(from (1))
Put in 2
8−4y
2
−2y
2
=2
6y
2
=6
y
2
=1
⇒y=+1,−1x=4,4
Point (4,1) and (4,−1)
The angle of the intersection of two curves is the angle between tangent at their point of intersection.
Let m
1
and m
2
be the slope of tangent at point of intersection
m
1
=−
8y
2x
=−
4y
x
m
2
=
4y
2x
=
2y
x
for (4,1)
m
1
=
4
−4
=−1
m
2
=
2
4
=2
tanθ=
∣
∣
∣
∣
∣
1+m
1
m
2
m
1
−m
2
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
1−2
−1−2
∣
∣
∣
∣
∣
=3
θ=tan
−1
3
Step-by-step explanation:
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