Question

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

Answer 1

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}`