Question

Which equation represents a circle with a center at (-4, 9) and a diameter of 10 units?

BEOO
(x - 9)2 + (y + 4)2 =
(x +4)2 + (y - 9)2 =
(x - 9)2 + (y + 4)2 = 100
(x + 4)2 + (y – 9)2 = 100
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Answer 1

Answer:B

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Answer 2

Therefore,

`(x+4)^(2)+(y-9)^(2)=25`

Explanation:

Given:

Let the Center be

C (h , k)=(-4 , 9)

Diameter = d = 10 units

∴
`Radius=(Diameter)/(2)=(10)/(2)=5\ units`

To Find:

Equation of Circle =?

Solution:

The Equation of the Circle with the center at (h, k) and the radius r is given by

`(x-h)^(2)+(y-k)^(2)=r^(2)`

Where,

C (h , k)=(-4 , 9) = Center

r = radius

Substituting the values we get

`(x-(-4))^(2)+(y-9)^(2)=5^(2)`

`(x+4)^(2)+(y-9)^(2)=25` ...AS required

Therefore,

`(x+4)^(2)+(y-9)^(2)=25`