Math, asked by yova, 4 months ago

Let the length of the normal chord through P on the ellipsoid is equal to 4 PG, where

G is the point at which the normal cuts the xy-plane. Find the surface where the point

P lies.​

Answers

Answered by pratham7777775
6

Step-by-step explanation:

define r.m.s value of current in ac circuit? give the relation between r.m.s value and peak value of current in a.c circuit

Answered by Itz2minback
3

Answer:

Normal at point P(acosθ,bsinθ) is

cosθ

ax

sinθ

by

=a

2

−b

2

(i)

It meets axes at Q(

a

(a

2

−b

2

)cosθ

,0)

and R(0,−

b

(a

2

−b

2

)sinθ

)

Let T(h,k) is a midpoint of QR.

Then 2h=

a

(a

2

−b

2

)cosθ

and 2k=−

b

(a

2

−b

2

)sinθ

⇒cos

2

θ+sin

2

θ=

(a

2

−b

2

)

2

4h

2

a

2

+

(a

2

−b

2

)

2

4k

2

b

2

=1

⇒ Locus is

4a

2

(a

2

−b

2

)

2

x

2

+

4b

2

(a

2

−b

2

)

2

y

2

=1 (ii)

which is an ellipse, having eccentricity e

, given by

e

′2

=1−

4b

2

(a

2

−b

2

)

2

4a

2

(a

2

−b

2

)

2

=1−

a

2

b

2

=e

2

e

=e

Note : In Equation (ii),

4a

2

(a

2

−b

2

)

<

4b

2

(a

2

−b

2

)

. Hence, x-axis is minor axis.

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