Question

Please help fast!!!! What are the center and radius of the circle defined by the equation x2 + y2 - 6x+By+21=0 ?

Answer 1

Option A

Explanation:

The first thing we want to do here is to rewrite the equation given to us, in standard circle equation -

`x^2+y^2-6x+8y+21=0,\\\left(x-3\right)^2+\left(y-\left(-4\right)\right)^2=2^2`

The " standard form " of a circle is given to be in the following form,
`(x-a)^(2) + (y-b)^(2) = r^2` where r = radius, centered at ( a, b )

Now as you can see, the center ( given by ( a, b ) ) should be ( 3, - 4 ). Respectively the radius is 2, and therefore the circle properties are -

Center
`( 3, - 4 )`; radius
`2`

Hope that helps!