Question

a circle has a center at C -1, 6 and the point on the circle has coordinates a 4, negative 6 . could the point B lie on the same Circle if it lies at being negative 6, 18

Answer 1

Step-by-step explanation:

The equation of a circle with center (x1, y1) is:

`(x-x_1)^2+(y-y_1)^2=r^2`

Where r is the radius of the circle.

In this problem the equation is:

`(x+1)^2+(y-6)^2=r^2`

To find the radius r we have to replace the coordinates of point A(4, -6) into the equation:

`\begin{gathered} (4+1)^2+(-6-6)^2=r^2 \\ 5^2+12^2=r^2 \\ 25+144=r^2 \\ r^2=169 \end{gathered}`

Therefore, the complete equation of this circle is:

`(x+1)^2+(y-6)^2=169`

To find if point B(-6, 18) lies on the same circle we have to replace x = -6 and y = 18 into the equation above. If the equality is true, then the point lies on the circle:

`\begin{gathered} (-6+1)^2+(18-6)^2=169 \\ (-5)^2+12^2=169 \\ 25+144=169 \\ 169=169\text{ --> true} \end{gathered}`

Answer:

Point B lies on the same circle