Question

Find the equation of the circle whose center and radius are given.

center ( 7, -3), radius = 7

Answer 1

(x – h)² + (y – k)² = r²

Fill in the numbers

(x – 7)² + (y +3)² = 49

Answer 2

Answer: The required equation of the circle is
`x^2+y^2-14x+6y+9=0.`

Step-by-step explanation: We are given to find the equation of the circle with center at the point (7, -3) and radius of length 7 units.

We know that

the standard equation of a circle with center at the point (h, k) and radius of length r units is given by

`(x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

For the given circle,

center, (h, k) = (7, -3) and radius, r = 7 units.

From equation (i), we get

`(x-7)^2+(y-(-3))^2=7^2\\\\\Rightarrow (x-7)^2+(y+3)^2=49\\\\\Rightarrow x^2-14x+49+y^2+6y+9=49\\\\\Rightarrow x^2+y^2-14x+6y+9=0.`

Thus, the required equation of the circle is
`x^2+y^2-14x+6y+9=0.`