Question

Find an equation for a circle with center (-5,9), tagent to the y-axis

Answer 1

Explanation:

The equation of a circle is

`(x - h) {}^(2) + (y - k) {}^(2) = {r}^(2)`

where (h,k) is center and r is the radius

We know h is -5 and k is 9

`( x + 5) {}^(2) + (y - 9) {}^(2) = {r}^(2)`

The point of tangency is perpendicular to the radius of the circle and lies on the circle circumference

We know the point of tangency lies on the y axis so that means the point is (0,k) where k is some number.

Solving for k requires some analytical skills.

The shortest distance between two points are points that are perpendicular to each other.

The pernediuclar line to x=0(the y axis) is y=k, the y coordinate of the point of tangency should be the same as the y coordinate of the center( which is 9,

so k=9

Therefore our point of tangency is (0,9)

The distance between the center and the point of tangency is 5, thus our radius is 5

So our equation is

`(x + 5) {}^(2) + (y - 9) {}^(2) = 25`