Question

URGENT 50 PTS AND BRAINLIEST FOR A CORRECT ANSWER THAT EXPLAINS WELL

Answer 1

Answer:

A. $(x+5)^2+(y-4)^2=16$

B. $(x-1)^2+(y-4)^2=2$

C. $\left(x-3\right)^2+\left(y-5\right)^2=9$

Step-by-Step Explanation:

A. Tangent to x-axis, r=4, contains (-5,8)

The equation of a circle is this: $(x-h)^2+(y-k)^2=r^2$

Therefore, we know that our equation will be: $(x-h)^2+(y-k)^2=4^2=16$

Because the circle is tangent to the x-axis, the point (-5,8) will be the top of the circle.

Therefore, the center is (-5,4), where -5=h and 4=k.

The answer is $(x+5)^2+(y-4)^2=16$

B. Diameter endpoints (2,5) and (0,3)

To solve for the diameter, we can use this equation: $d=\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2 }$

$d=\sqrt{(2-0)^2+(5-3)^2 }\\\\d=\sqrt{2^2+2^2}=\sqrt{4+4} =\sqrt{8}= 2\sqrt{2}$

Because the radius is half of the diameter, $r=\sqrt{2}$

Therefore, we know that our equation will be: $(x-h)^2+(y-k)^2=(\sqrt{2}) ^2=2$

Then, we can decipher that h=1, as the midpoint of 0 and 2 is 1, and k=4, as the midpoint of 3 and 5 is 4.

The answer is $(x-1)^2+(y-4)^2=2$

C. Center on x=3, tangent to y-axis at (0,5)

We can see that the center is (3,5). Therefore, the equation is $(x-3)^2+(y-5)^2=r^2$

To solve for r, we can substitute the point (0,5) into the equation.

$(0-3)^2+(5-5)^2=r^2\\(-3)^2+(0)^2=r^2\\r^2=9$

The answer is $(x-3)^2+(y-5)^2=9$

Hope this helped!