# Choose the correct option from the given alternatives: The differential equation of all circles having their centres on the line y = 5 and touching the X-axis is - Mathematics and Statistics

MCQ

Choose the correct option from the given alternatives:

The differential equation of all circles having their centres on the line y = 5 and touching the X-axis is

#### Options

• "y"^2 (1 + "dy"/"dx") = 25

• ("y - 5")^2 [1 + ("dy"/"dx")^2] = 25

• ("y - 5")^2 + [1 + ("dy"/"dx")^2] = 25

• ("y - 5")^2 [1 - ("dy"/"dx")^2] = 25

#### Solution

("y - 5")^2 [1 + ("dy"/"dx")^2] = 25

Hint: Equation of the circle is

(x - h)2 + (y - 5)2 = 52      ....(1)

∴ 2(x - h) + 2(y - 5)"dy"/"dx" = 0

∴ (x - h)2 = (y - 5)2 ("dy"/"dx")^2

∴ 25 - (y - 5)2 = (y - 5)2 ("dy"/"dx")^2    ...[By (1)]

∴ (y - 5)2 [1 + ("dy"/"dx")^2] = 25

Concept: Formation of Differential Equations
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 6 Differential Equations
Miscellaneous exercise 6 | Q 1.04 | Page 215