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Application Of Derivatives

Question
CBSEENMA12036166
Wired Faculty App

The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is 

  • (x – 2)y′2 = 25 – (y – 2)2 

  • (y – 2)y′2 = 25 – (y – 2)2

  • (y – 2)2y′2= 25 – (y – 2)2 

  • (x – 2)2y′2= 25 – (y – 2)2

Solution

C.

(y – 2)2y′2= 25 – (y – 2)2 

(x – h)2 + (y – 2)2 = 25
rightwards double arrow space 2 space left parenthesis straight x plus negative straight h right parenthesis space plus space 2 left parenthesis straight y minus 2 right parenthesis space dy over dx space equals space 0 rightwards double arrow space left parenthesis straight x minus straight h right parenthesis space equals space minus space left parenthesis straight y minus 2 right parenthesis dy over dx substituting space in space left parenthesis 1 right parenthesis space we space have left parenthesis straight y minus 2 right parenthesis squared space open parentheses dy over dx close parentheses squared space plus space left parenthesis straight y minus 2 right parenthesis squared space equals space 25 left parenthesis straight y minus 2 right parenthesis squared straight y squared space equals space 25 minus left parenthesis straight y minus 2 right parenthesis squared

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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