Question

3. Write the equation of the circle with a center at (-6, 1) and an area of 7n.

A Q(x + 6)^2 + (y - 1)^2 = 14
B (x - 6)^2 + (y + 1)^2 = 49
C (x + 6)^2 + (y - 1)^2 = 49
D (x + 6)^2 + (y - 1)^2 = 7
E (x - 6)^2 + (y + 1)^2 = 7

Answer 1

The correct equation of a circle with a center at (-6, 1) and an area of 7π is (x + 6)² + (y - 1)² = 49, which corresponds to option C.

Step-by-step explanation:

The question is asking to write the equation of a circle given the center and the area of the circle. The center of the circle is at (-6, 1). Since the area of a circle is given by πr², the radius can be found by rearranging this area formula to r = √(Area/π). The area is given as 7π, so the radius r is √(7π/π) = √7. The equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. The correct equation in this case is (x + 6)² + (y - 1)² = 49, since 49 is 7². Therefore, the correct answer is C.

Answer 2

D
`(x +6) ^2 +(y-1)^2 =7`

Step-by-step explanation:

Center of the circle (h, k) = (-6, 1)

Area of the circle
`=\pi r^2`

`7\pi=\pi r^2`

`\frac {7\pi}{\pi} =r^2`

`r^2=7`

`r=\sqrt 7`

Radius
`r=\sqrt {7}`

Equation of circle in center radius form is given as:

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

Plugging the values of h, k and r in the above equation, we find:

`[x - (- 6)] ^2 +[y-1 ]^2 =(\sqrt {7})^2`

`(x +6) ^2 +(y-1)^2 =7`