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Find all real numbers a such that the given point is on the circle x2 + y2 = 1.8gia

Find all real numbers a such that the given point is on the circle x2 + y2 = 1.8gia-example-1
User Sernle
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1 Answer

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Let the coordinate be as follows.


(x,y)=\mleft(-(8)/(9),a\mright)

Substitute the coordinates into the equation.


\mleft(-(8)/(9)\mright)^2+a^2=1

Simplify the left side of the equation.


(64)/(81)+a^2=1

Subtract both sides of the equation by 64/81.


\begin{gathered} a^2=1-(64)/(81) \\ =(81)/(81)-(64)/(81) \\ =(17)/(81) \end{gathered}

To obtain the value of a, use the square root property. Find the square root of both sides of the equation.


a=\pm\sqrt[]{(17)/(81)}=\pm\frac{\sqrt[]{17}}{9}

Thus, the values of a is as follows.


a=\frac{\sqrt[]{17}}{9}\text{and -}\frac{\sqrt[]{17}}{9}

User Dharam
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