The smallest circle with centre on Y-axis and passing through the point `(7,3)` has radius

Options

A. `sqrt(58)`
B. 7
C. 3
D. 4

Answer

B

Explanation

Let the centre of circle on Y-axis be `(0,k)`
Let `d=sqrt((7-0)^(2)+(3-k)^(2))`
`impliesd^(2)=7^(2)+(3-k)^(2)=D`
On differentiating w.r.t we get
`(dD)/(dk)=0+2(3-k)(-1)`
Put `(dD)/(dk)=0`
`impliesk=3`
Now `(d^(2)D)/(dk^(2))=2gt0` Minima,
`:.` Minimum value at `k=3` is `d=7`.
Hence minimum radius of circle 7.