Maths-
General
Easy

Question

x squared minus 8 x plus y squared minus 10 y equals 40
In the xy-plane, the graph of the given equation is a circle. What is the radius of this circle?

The correct answer is: 9


    The general equation for a circle is left parenthesis x minus h right parenthesis squared plus left parenthesis y minus k right parenthesis squared equals r squared, where (h. k) is the center and r is a radius.
    Explanations:
    Step 1 of 2:
    The given equation for the circle is x squared minus 8 x plus y squared minus 10 y equals 40
    Now, x squared minus 8 x plus y squared minus 10 y equals 40
    not stretchy rightwards double arrow x squared minus 2 times x times 4 plus left parenthesis 4 right parenthesis squared plus y squared minus 2 times y times 5 plus left parenthesis 5 right parenthesis squared equals 40 plus left parenthesis 4 right parenthesis squared plus left parenthesis 5 right parenthesis squared
    not stretchy rightwards double arrow left parenthesis x minus 4 right parenthesis squared plus left parenthesis y minus 5 right parenthesis squared equals 40 plus 16 plus 25 equals 81 equals left parenthesis 9 right parenthesis squared times horizontal ellipsis left parenthesis ∗ right parenthesis
    Step 2 of 2:
    Now comparing equation (*) with the general equation for circle, we get r = 9.
    Final Answer:
    The radius of the circle is 9 unit.

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