Question

Find find the centre and radius of the circle.
x² + y² - 4x - 8y - 45 = 0.​

Answer 1

⠀⠀ıllıllı uoᴉʇnloS ıllıllı

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The equation of the given circle is x² + y² - 4x - 8y - 45 = 0.

${x}^{2} + {y}^{2} - 4x - 8y - 45 \\ = > ( {x}^{2} - 4x) + ({y}^{2} - 8) = 45 \\ = > {x}^{2} - 2(x)(2) + {2}^{2} + {y}^{2} - 2(y)(4) + {4}^{2} - 4 - 16 = 45 \\ = > (x - 2)2 \: + (y - 4)2 = 65 \\ = > (x - 2)2 + (y - 4)2 = ( \sqrt{65) } { }^{2} \\ \\ Which \: is \: of \: the \: form \: (x - h)^{2} + (y - k) ^{2} = r ^{2} , \: Where,$

• h = 2
• k = 4
• r = $\sqrt{65}$

Thus, The centre of the given circle is (2, 4), while its radius is $\sqrt{65}$

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