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Mathematics

Grade9

Easy

Question

Write the standard equation of the circle with center (1, 4) and radius 4.

$(x - 1)^{2} + (y + 4)^{2} = 1$
$(x - 4)^{2} + (y + 1)^{2} = 4$
$(x + 1)^{2} + (y + 4)^{2} = 9$
$(x - 1)^{2} + (y - 4)^{2} = 16$

hint Hint:

The standard equation of a circle with center (h, k) and radius r is: $left parenthesis x minus h right parenthesis squared plus left parenthesis y minus k right parenthesis squared equals r squared$ . substitute the given values to find the standard equation of the circle.

The correct answer is: $left parenthesis x minus 1 right parenthesis squared plus left parenthesis y minus 4 right parenthesis squared equals 16$

The standard equation of a circle with center (h, k) and radius r is: $left parenthesis x minus h right parenthesis squared plus left parenthesis y minus k right parenthesis squared equals r squared$
If the centre is (1, 4) and radius is 4.
So, the equation of circle is $left parenthesis x minus 1 right parenthesis squared plus left parenthesis y minus 4 right parenthesis squared equals left parenthesis 4 right parenthesis squared rightwards double arrow$ $left parenthesis x minus 1 right parenthesis squared plus left parenthesis y minus 4 right parenthesis squared equals 16$
Therefore, $left parenthesis x minus 1 right parenthesis squared plus left parenthesis y minus 4 right parenthesis squared equals 16$ is the standard equation of the circle with center (1, 4) and radius 4.

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