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ગણિત ધોરણ 11 સેમિસ્ટર 2

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નીચે આપેલ કેન્દ્ર અને ત્રિજ્યાવાળા વર્તુળના સમીકરણ મેળવો :

કેન્દ્ર : (-1, 1)

ત્રિજ્યા : square root of 2


અહીં, કેન્દ્ર (-1, 1) અને ત્રિજ્યા square root of 2 છે.

વર્તુળનું સમીકરણ,

open parentheses straight x space minus open parentheses negative 1 close parentheses close parentheses squared space plus space open parentheses y space minus space 1 close parentheses squared space equals space open parentheses square root of 2 close parentheses squared

rightwards double arrow space x squared space plus space 2 x space plus space 1 space plus space y squared space minus space 2 y space plus space 1 space equals space 2

rightwards double arrow space x to the power of bold 2 bold space bold plus bold space bold italic y to the power of bold 2 bold space bold plus bold space bold 2 bold italic x bold space bold minus bold space bold 2 bold italic y bold space bold equals bold space bold 0


નીચે આપેલ કેન્દ્ર અને ત્રિજ્યાવાળા વર્તુળના સમીકરણ મેળવો :

કેન્દ્ર : (-2, 3)

ત્રિજ્યા : 5


અહીં, કેન્દ્ર (-2, 3) અને ત્રિજ્યા 5 છે.

વર્તુળનું સમીકરણ,

open parentheses straight x space minus space open parentheses negative 2 close parentheses close parentheses squared space plus space open parentheses straight y space minus space 3 close parentheses squared space equals space 5 squared

rightwards double arrow space straight x squared space plus space 4 straight x space plus space 4 space plus space straight y squared space minus 6 straight y space plus space 9 space equals space 25

rightwards double arrow bold space bold x to the power of bold 2 bold space bold plus bold space bold y to the power of bold 2 bold space bold plus bold space bold 4 bold x bold space bold minus bold space bold 6 bold y bold space bold minus bold space bold 12 bold space bold equals bold space bold 0


નીચે આપેલ કેન્દ્ર અને ત્રિજ્યાવાળા વર્તુળના સમીકરણ મેળવો :

કેન્દ્ર : open parentheses square root of 2 comma space minus square root of 5 close parentheses

ત્રિજ્યા : square root of 5


અહીં, કેન્દ્ર open parentheses negative square root of 2 comma space minus square root of 5 close parentheses અને ત્રિજ્યા square root of 5  છે.

વર્તુળનું સમીકરણ,

open parentheses straight x space minus space open parentheses negative square root of 2 close parentheses close parentheses squared space plus space open parentheses y space minus space open parentheses negative square root of 5 close parentheses close parentheses squared space equals space open parentheses square root of 5 close parentheses squared

rightwards double arrow space x squared space plus space 2 square root of 2 x space plus space 2 space plus space y squared space plus space 2 square root of 5 y space plus space 5 space equals space 0

rightwards double arrow bold space bold italic x to the power of bold 2 bold space bold plus bold space bold italic y to the power of bold 2 bold space bold plus bold space bold 2 square root of bold 2 bold space bold italic x bold space bold plus bold space bold 2 bold space square root of bold 5 bold space bold italic y bold space bold plus bold space bold 2 bold space bold equals bold space bold 0


નીચે આપેલ કેન્દ્ર અને ત્રિજ્યાવાળા વર્તુળના સમીકરણ મેળવો :

કેન્દ્ર : open parentheses negative 4 space cos space straight alpha comma space 4 space sin space straight alpha close parentheses

ત્રિજ્યા : 5


અહીં, કેન્દ્ર open parentheses negative 4 space cos space straight alpha comma space 4 space sin space straight alpha close parentheses અને ત્રિજ્યા 5 છે.

વર્તુળનું સમીકરણ,

open parentheses straight x space minus space open parentheses negative 4 space cos space straight alpha close parentheses close parentheses squared space plus space open parentheses y space minus space 4 space sin space alpha close parentheses squared space equals space 5 squared

rightwards double arrow space x squared space plus space 8 x space cos space alpha space plus space 16 space cos squared space alpha space plus space y squared space minus space 8 y space sin space alpha space plus space 16 space sin squared space alpha space equals space 25

rightwards double arrow space x squared space plus space y squared space plus space 8 x space cos space alpha space minus space 8 y space sin space alpha space plus space 16 space open parentheses cos squared space alpha space plus space sin squared space alpha close parentheses space equals space 25

rightwards double arrow space x squared space plus space y squared space plus space 8 x space cos space alpha space minus space 8 y space sin space alpha space plus space 16 space minus space 25 space equals space 0

rightwards double arrow bold space bold italic x to the power of bold 2 bold space bold plus bold space bold italic y to the power of bold 2 bold space bold plus bold space bold 8 bold italic x bold space bold italic c bold italic o bold italic s bold space bold italic alpha bold space bold minus bold space bold 8 bold italic y bold space bold italic s bold italic i bold italic n bold space bold italic alpha bold space bold minus bold space bold 9 bold space bold equals bold space bold 0


નીચે આપેલ કેન્દ્ર અને ત્રિજ્યાવાળા વર્તુળના સમીકરણ મેળવો :

કેન્દ્ર : (1, 0)

ત્રિજ્યા : 1


અહીં, કેન્દ્ર (1, 0) અને ત્રિજ્યા 1 છે.

વર્તુળનું સમીકરણ,

open parentheses straight x space minus space 1 close parentheses squared space plus space open parentheses y space minus space 0 close parentheses squared space equals space 1 squared

therefore space x squared space minus space 2 x space plus space 1 space plus space y squared space equals space 1

therefore bold space bold italic x to the power of bold 2 bold space bold plus bold space bold italic y to the power of bold 2 bold space bold minus bold space bold 2 bold italic x bold space bold equals bold space bold 0