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Mathematics Test 39

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Mathematics Test 39
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    The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is

    Solution

    Equation of circle is 
    x2 + y2 + 2x + 4y – 3 = 0 
    centre ≡ (–1, –2) 
    Let Q(α, β) is the point diametrically opposite on the given circle. 
    i.e., P(1, 0), C(–1, –2) & Q(α, β) 
    – 1 = (1+α)/2  ⇒ α = – 3 
    – 2 = (0+β)/2 ⇒ β = –4 

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