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The circle below has center P.The point (x, y) is on the circle as shown.12-(a) Find the following.1110-unitsRadius: 0Center: 0987Value of a:(Choose one)(x,y)351Value of b:(Choose one)4a32(b) Use the Pythagorean Theorem to write an equationrelating the side lengths of the right triangle. Writeyour answer in terms of x and y (with no otherletters)+

The Circle Below Has Center PThe Point X Y Is On The Circle As Shown12a Find The Following1110unitsRadius 0Center 0987Value Of AChoose Onexy351Value Of BChoose class=

Sagot :

Given:

Center of the circle = P

Let's determine the following:

a) Radius.

Here, the radius of the circle is the hypotenuse of the triangle.

Therefore, the radius of the circle is 3 units

b) Center:

To find the point at the center of the circle, let's locate the point P on the graph.

On the graph, the point P is at (x, y) ==> (9, 4)

Therefore, the center (h, k) is (9, 4)

c) Value of a:

To find the value of a, let's first find the value of b.

Value of b = 6 - 4 = 2

Apply Pythagorean Theorem to find the value of a:

[tex]c^2=a^2+b^2[/tex]

Where:

c is the hypotenuse = 3

b = 2

Thus, we have:

[tex]\begin{gathered} 3^2=a^2+2^2 \\ \\ 9=a^2+4 \\ \\ \text{Subtract 4 from both sides:} \\ 9-4=a^2+4-4 \\ \\ 5=a^2 \\ \\ \text{Take the square root of both sides:} \\ \sqrt[]{5}=\sqrt[]{a^2} \\ \\ 2.2=a \\ \\ a=2.2 \end{gathered}[/tex]

Therefore, the value of a is 2.2 units

d) Value of b.

The value of b is 2 units

ANSWERS:

• Radius: , 3 units

,

• Center: , (9, 4)

,

• Value of a = , 2.2 units

,

• Value of b = , 2 units

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