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8. (a) Find the equation of circle having (x), y1) and (x2,y21 as theends of diameter. |
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Answer» find the equation of circle whose diameter is join of the point (x₁,y₁) and (x₂, y₂) . Let A ≡ (x₁,y₁) and B ≡ (x₂,y₂)Then, equation of circle is given by (x - x₁)(x - x₂) +(y - y₁)(y - y₂) = 0 [ by formula ] x² - (x₁ + x₂)x + x₁x₂ + y² - (y₁ + y₂)y + y₁y₂ = 0x² + y² -(x₁ + x₂)x - (y₁ + y₂)y + x₁x₂ + y₁y₂ = 0 Hence, the equation of circle is x² + y² -(x₁ + x₂)x - (y₁ + y₂)y + x₁x₂ + y₁y₂ = 0 |
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