Question

How do you write an equation for a circle given center (-8,-7) and tangent to the y-axis?

Answer 1

`(x+8)^2+(y+7)^2=64`

Explanation:

The standard form of the equation of a circle is.

`color(red)(bar(ul(|color(white)(a/a)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(a/a)|)))`
where (a ,b) are the coordinates of the centre and r, the radius.

here centre = (-8 ,-7) `rArra=-8" and " b=-7`

Since the y-axis is a tangent then the radius will be the horizontal distance from (-8 ,-7) to the y-axis ( x = 0). That is radius = 8.

substitute values into the standard equation.

`(x-(-8))^2+(y-(-7))^2=8^2`

`rArr(x+8)^2+(y+7)^2=64" is the equation of the circle"`
graph{(x+8)^2+(y+7)^2=64 [-31.6, 31.6, -15.8, 15.8]}