Answer:
[tex]\text{A) }x^2+y^2=25[/tex]
Step-by-step explanation:
The equation of a circle with center [tex](h, k)[/tex] and radius [tex]r[/tex] is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex].
We're given:
- The circle's center is at the origin (0, 0)
- The point (-3, 4) is on the circle
Since we're given the circle's center, we just need to find the radius. Because the center of the circle is at (0, 0), the radius will be equal to the distance from (-3, 4) and (0, 0).
For points [tex](x_1, x_2)[/tex] and [tex](x_2, y_2)[/tex], the distance between them is given by the formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let:
[tex](x_1, y_1)\implies (0, 0)\\(x_2, y_2)\implies (-3, 4)[/tex]
The distance between these two points must be:
[tex]d=\sqrt{(-3-0)^2+(4-0)^2},\\d=\sqrt{9+16},\\d=\sqrt{25},\\d=5[/tex]
Therefore, the radius of the circle is 5 and the equation of the circle is:
[tex](x-0)^2+(y-0)^2=5^2,\\\boxed{x^2+y^2=25}[/tex]
