Question

A circle in the xy-plane has center (5, 7) and radius 2. Which of the following is an equation of the circle?

Answer 1

the option (d) satisfies the conditions of your answer

it's centre is (5,7) (put the values in the equation

the general equation of the circle is x^2+y^2=r^2

so the radius is 2 so the option will be (d)

Answer 2

SoluTion :-

Equation of a circle

$\sf {(x-a)^{2}+(y-b)^{2}=r^{2}}$

Where a is the x-coordinate for the centre of the circle, b is the y-coordinate of the centre of the circle, and r is the radius.

Since radius of Circle = 2. Therefore,

$\sf {r^{2}=2^{2}=4}$

Now,

$\sf {(x-a)^{2}+(y-b)^{2}=4}$

Substituting a and b for the values given as the circle's centre,

$\sf {a=5}\\\\\\\sf {b=7}\\\\\\\\\sf {(x-5)^{2}+(y-z)^{2}=4}$