Gujarati
10-1.Circle and System of Circles
hard

उस वृत्त का समीकरण जो वृत्तों ${x^2} + {y^2} + x + 2y + 3 = 0$, ${x^2} + {y^2} + 2x + 4y + 5 = 0$ व ${x^2} + {y^2} - 7x - 8y - 9 = 0$ को समकोण पर काटता है, होगा

A

${x^2} + {y^2} - 4x - 4y - 3 = 0$

B

$3({x^2} + {y^2}) + 4x - 4y - 3 = 0$

C

${x^2} + {y^2} + 4x + 4y - 3 = 0$

D

$3({x^2} + {y^2}) + 4(x + y) - 3 = 0$

Solution

(d) माना वृत्त ${x^2} + {y^2} + 2gx + 2fy + c = 0$ है।

$g + 2f = c + 3$….$(i)$

$2g + 4f = c + 5$….$(ii)$

$ – 7g – 8f = c – 9$….$(iii)$

$ \Rightarrow g = \frac{2}{3},\;f = \frac{2}{3},\;c =  – 1$

अत: अभीष्ट समीकरण $3({x^2} + {y^2}) + 4(x + y) – 3 = 0$ है।

Standard 11
Mathematics

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