Mathematics
Grade-8
Easy

Question

Match the function (x+4)2 + (y + 3)2= 16 to the graph

Hint:

We will substitute the points on given graphs to find which graph represents the given function.

The correct answer is:


    GIVEN-
    (x+4)2 + (y + 3)2= 16
    TO FIND-
    Graph of the given function.
    SOLUTION-
    In the given function, for x = -4-
    (x + 4)2 + (y + 3)2 = 16
    ∴           (-4 + 4)2 + (y + 3)2 = 16
    ∴                  (0)2 + (y + 3)2 = 16
    ∴        0 + y2 + 2(y)(3) + 32 = 16
    ∴                      y2 + 6y + 9 = 16
    ∴               y2 + 6y + 9 - 16 = 0
    ∴                       y2 + 6y - 7 = 0
    ∴                  y2 + 7y - y - 7 = 0
    ∴          y (y + 7) - 1 (y + 7) = 0
    ∴                   (y - 1) (y + 7) = 0
    ∴ either y - 1 = 0 or y + 7 = 0
    ∴ either y = 1 or y = -7
    Thus, (-4,1) and (-4,-7) should be 2 points on the given graph.
    This condition is satisfied in option d only.
    FINAL ANSWER-
    Option 'd' is the correct answer to the given question.

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