Question

find the equation of the circle with centre C(-1/2,-9) and radius r=5​

Answer 1

Answer: The equation of the circle is...

$3x^{2} +3y^{2} -3x -54y -223 =0$

Step-by-step explanation: Centre of the circle=(-f/2,-g/2)=>(-1/2,-9)

substitute it in the basic circle equation

and the with the formula$\sqrt{f^{2}+g^{2}-c }= radius$ find "C"

I HOPE THIS HELPS......

Answer 2

The Equation of the circle is $4x^2+ 4y^2 + 4x + 72 y +225=0$

Given,

Centre of the circle (C) = (-1/2,-9)

The radius of the Circle (r) = 5​

To Find,

The equation of the circle.

Solution,

A closed curve that is drawn from a fixed point called the center, in which all the points on the curve have the same distance from the center point of the center is called a circle.

The standard equation of a circle is given by:

$(x-h)^{2} + (y-k)^2 = r^2$

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

Putting the given values in the standard equation of the circle:

$\implies (x-(\frac{-1}{2} ))^{2} + (y-(-9))^2 = 5^2\\\\\implies (x+\frac{1}{2} )^{2} + (y+9)^2 = 25\\\\\implies x^2+\frac{1}{4} + (2\cdot x \cdot \frac{1}{2} ) + y^2+81+ (2\cdot y \cdot 9 ) = 25\\\\\implies x^2+\frac{1}{4} + x + y^2+81+ 18 y = 25\\\\\implies x^2+ y^2 + x + 18 y +\frac{1}{4}+81-25=0\\\\\implies 4x^2+ 4y^2 + 4x + 72 y +225=0$

Therefore the required equation is $4x^2+ 4y^2 + 4x + 72 y +225=0$

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