Vector Algebra

Question

Represent the following family of curves by forming the corresponding differential equations (a. b: parameters).
$left parenthesis straight x minus straight a right parenthesis squared minus straight y squared space equals space 1$

Solution

The equation of given curve is
(x – a)² – y² = 1 ...(1)
Differentiating both sides w.r.t x, we get.
$2 left parenthesis straight x minus straight a right parenthesis minus 2 straight y dy over dx equals 0$ or $straight x minus straight a space equals space straight y dy over dx$
Putting value of x – a in (1), we get,
$straight y squared open parentheses dy over dx close parentheses squared minus straight y squared space equals space 1$
which is required differential equation.

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Vector Algebra

Represent the following family of curves by forming the corresponding differential equations (a. b: parameters).
$left parenthesis straight x minus straight a right parenthesis squared minus straight y squared space equals space 1$

Some More Questions From Vector Algebra Chapter

Determine order and degree (if defined) of differential equations:
y' + y = e^x

Determine order and degree (if defined) of differential equations:
y'' + (y')² + 2 y = 0

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Vector Algebra

Represent the following family of curves by forming the corresponding differential equations (a. b: parameters).

Some More Questions From Vector Algebra Chapter

Determine order and degree (if defined) of differential equations:y' + y = ex

Determine order and degree (if defined) of differential equations:y'' + (y')2 + 2 y = 0

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Represent the following family of curves by forming the corresponding differential equations (a. b: parameters).
$left parenthesis straight x minus straight a right parenthesis squared minus straight y squared space equals space 1$

Determine order and degree (if defined) of differential equations:
y' + y = e^x

Determine order and degree (if defined) of differential equations:
y'' + (y')² + 2 y = 0