Represent the following family of curves by forming the corresponding differential equations (a. b: parameters).
$straight y squared minus 4 straight a left parenthesis straight x minus straight b right parenthesis$

Solution

The equation of given curve is
y² = 4 a (x – b)
Differentiating w.r.t. x, we get,
$2 straight y dy over dx space equals space 4 space straight a$ or $straight y dy over dx space equals 2 straight a$
Again differentiating w.r.t x, we get.
$straight y fraction numerator straight d squared straight y over denominator dx squared end fraction plus dy over dx. dy over dx space equals space 0$ or $straight y fraction numerator straight d squared straight y over denominator dx squared end fraction plus open parentheses dy over dx close parentheses squared space equals space 0$
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).
$straight y squared minus 4 straight a left parenthesis straight x minus straight b right parenthesis$

Some More Questions From Vector Algebra Chapter

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

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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Represent the following family of curves by forming the corresponding differential equations (a. b: parameters).
$straight y squared minus 4 straight a left parenthesis straight x minus straight b right parenthesis$

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