Question

I need help with 2 questions, I don't understand how to do them. Any help would be greatly appreciated!

Answer 1

The length of CE is 3.6 and the radius of the circle is 2

The length of CE

Start by calculating the length of AD using:

AD^2 = AC^2 - CD^2

This gives

AD^2 = 10^2 - 6^2

AD^2 = 64

Take the square roots

AD = 8

Represent CE with x.

So:

AE = 10 - x

Calculate ED using:

ED^2 = CD^2 - CE^2

ED^2 = AD^2 - AE^2

So, we have:

AD^2 - AE^2 = CD^2 - CE^2

This gives

8^2 - (10 - x)^2 = 6^2 - x^2

Expand

64 - 100 + 20x - x^2 = 36 - x^2

Add x^2 to both sides

64 - 100 + 20x  = 36

Evaluate the like terms

20x = 72

Divide by 20

x = 3.6

Hence, the length of CE is 3.6

The radius of the circle

The equation is given as:

x^2 + y^2 + 6x + 5y = -45/4

Rewrite as:

x^2 + 6x + y^2  + 5y = -45/4

Take the coefficients of x and y

Divide them by 2, square the result and add the result to both sides.

So, we have:

x^2 + 6x + (6/2)^2 + y^2  + 5y + (5/2)^2= -45/4+ (6/2)^2 + (5/2)^2

This gives

x^2 + 6x + (6/2)^2 + y^2  + 5y + (5/2)^2= 4

Express as perfect squares

(x + 3)^2 + (y + 5/2)^2 = 4

The circle equation is represented as:

(x - a)^2 + (y - b)^2 = r^2

Where r represents the radius

By comparison, we have:

r^2 = 4

This gives

r = 2

Hence, the radius of the circle is 2

Read more about circle equation at:

brainly.com/question/10618691

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