Show that the following curves intersect orthogonally at the indicated points :
x2 = 4y and 4y + x2 = 8 at (2, 1)
Given:
Curves x2 = 4y ...(1)
& 4y + x2 = 8 ...(2)
The point of intersection of two curves (2,1)
Solving (1) & (2),we get,
First curve is x2 = 4y
Differentiating above w.r.t x,
⇒ 2x= 4.
⇒ 
⇒ m1
...(3)
Second curve is 4y + x2 = 8
⇒ 4.
+ 2x = 0
⇒ 
⇒ m2
...(4)
Substituting (2,1) for m1 & m2,we get,
m1
⇒ 
m1 = 1 ...(5)
m2
⇒ 
m2 = – 1 ...(6)
when m1 = 1 & m2 = – 1
⇒ 1× – 1 = – 1
∴ Two curves x2 = 4y & 4y + x2 = 8 intersect orthogonally.
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