Question

A circle in the xy-plane has the equation: 3.5(x+2.2)²+3.5(y-11.1)²-21=0. What is the radius of the circle? Round the answer to the nearest hundredth.

a) 3.89
b) 4.22
c) 5.56
d) 6.01

Answer 1

The radius of the circle with the given equation is approximately 2.45 after rewriting the equation into the standard form and isolating the radius squared (r²) term.

Step-by-step explanation:

To find the radius of the circle described by the equation 3.5(x+2.2)²+3.5(y-11.1)²-21=0, we first need to rewrite the equation into the standard form of a circle's equation, which is (x - h)² + (y - k)² = r² where (h, k) is the center of the circle and r is the radius.

We can start simplifying the given equation by dividing all terms by 3.5:

• (x+2.2)² + (y-11.1)² = 6

Now, compare it to the standard form, we can see that:

• The left side is already in the correct form with h = -2.2 and k = 11.1.
• The right side is equal to r², so we have r² = 6.

To find the radius (r), we take the square root of 6:

• r = √6 ≈ 2.45

Therefore, the radius of the circle is approximately 2.45, which is not an option in the given choices. There may have been a mistake in copying the options or a miscalculation. Please double-check the given equation and the answer choices.