Show that the following curves intersect orthogonally at the indicated points :

y2 = 8x and 2x2 + y2 = 10 at (1, 2√2)

Given:


Curves y2 = 8x ...(1)


& 2x2 + y2 = 10 ...(2)


The point of intersection of two curves are (0,0) & (1,2)


Now ,Differentiating curves (1) & (2) w.r.t x, we get


y2 = 8x


2y.8



...(3)


2x2 + y2 = 10


Differentiating above w.r.t x,


4x + 2y. = 0


2x + y. = 0


y. = – 2x


...(4)


Substituting (1,2)for m1 & m2,we get,


m1



m1 = ...(5)


m2



m2 = ...(6)


when m1 & m2



×1


Two curves y2 = 8x & 2x2 + y2 = 10 intersect orthogonally.


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