Mathematics College

Which equation represents a circle with a center at (-4,9) and a diameter of 10 units?
(x - 9)2 + (+ 4)2 = 25
(x + 4)2 + (- 9)2 = 25
(x - 9)2 + ( + 4)2 = 100
(x + 4)2 + (- 9)2 = 100
PLZ HELP!

Answers

Answer 1
The first option is correct. See an explanation below.
Which Equation Represents A Circle With A Center At (-4,9) And A Diameter Of 10 Units?(x - 9)2 + (+ 4)2
Answer 2

The equation of circle with center at P ( -4 , 9 ) and diameter 10 units is given by ( x + 4 )² + ( y - 9 )² = 25

What is a Circle?

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

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

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

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the equation of circle be represented as A

Now , the value of A is

Let the center of the circle be P ( -4 , 9 )

Let the diameter of the circle be d = 10 units

So , the radius of the circle r = d/2 = 5 units

And , standard form of a circle is

( x - h )² + ( y - k )² = r²,

So , the equation of circle is

( x + 4 )² + ( y - 9 )² = 25

Hence , the equation of circle is ( x + 4 )² + ( y - 9 )² = 25

To learn more about equation of circle click :

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Answers

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Step-by-step explanation:

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