Dumb Question:

APPLICATION OF DERIVATIVES

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Dumb Question:

Dumb Question: How this derived ?
Ans: Let m₁ = tan

₁ =

m₂ = tan

₂ =

From fiq,

₁

₂ -

₁

Orthogonal curves: If angle of intersection of two curves is right angle, two curves are c/d orthogonal curves.

If curves are orthogonal,

Illustration: Find angle of intersection of curves y = x² & y = 4 - x²

For intersection points of given curves,

(x²) = 2x

(4 - x²) = - 2x

At x = -

= 2 x

= 2

= - 2

Both angles are equal.

Length of Tangent, Sub-Tangent, Normal & sub-Normal:
Length of Tangent: Length of segment PT of tangent b/w point of tangent & x-axis is c/d length of tangent.

PT =

Subtangent
: Projection of segment PT along x-axis i.e. St c/d subtangent.

Length of Normal
: Length of segment PN intercapted b/w point on curve r x-axis.
PN =

Subnormal
: Projection of segment PN along x-axis i.e. c/d subnormal.
SN = |y,

Dumb Question
: How these relation derived ?

Ans: Since PT makes angle

with x-axis, then
tan

Subtangent = ST = PS cot

But PS = y
₁
& cot

[see in fig.]

= cot(90 -

)

PS tan

Subnormal = SN =

Length of tangent = PT =

Length normal = PN =

Illustration
: Show that curve y = be
^x/a
. subnormal varies as square of ordinate ?

Ans:
[Dumb Question
: What is ordinate ?

Ans: y-axis component is c/d ordi i.e. in P(x
₁
, y
₁
)y
₁
is ordinate of point P.
y = be
^x/a
............................................... (i)
differentiating curve y = be
^x/a
w.r.t. x.