Please help me, circle chapter.

Mathematics

1 answer:

Ad libitum [116K]3 years ago

5 0

Answer: p = 4, r = 4

Step-by-step explanation:

The equation of a circle is: (x - h)² + (y - k)² = r² where

(h, k) is the center of the circle
r is the radius of the circle

Complete the square:

x² - 10x + _____ + y² + py + _____ = -13 + ___ + ___

x² - 10x + (-10/2)² + y² + py + (p/2)² = -13 + (-10/2)² + (p/2)²

(x - 5)² + (y + p/2)² = -13 + 25 + (p/2)²

↓ ↓ |_____↓_____|

h = 5 k = -p/2 r²

Given: (h, k) = (5, -2)

-2 = -p/2

-4 = -p

4 = p

r² = -13 + 25 + (p/2)²

= -13 + 25 + (4/2)²

= -13 + 25 + 4

= 16

$\sqrt{r^2}=\sqrt{16}$

r = 4

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Step-by-step explanation:

Let $f(\theta) = \frac{\sec \theta \cdot (\sec \theta+\tan \theta)}{1+\tan^{2}\theta}$ , we proceed to simplify the formula until a form based exclusively in sines and cosines is found. From Trigonometry, we shall use the following identities:

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Then, we simplify the given formula:

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