Question

What is the general form of the equation of the given circle with center A? A. X2 y2 6x − 24y − 25 = 0 B. X2 y2 − 6x 24y 128 = 0 C. X2 y2 6x – 24y 128 = 0 D. X2 y2 6x − 24y 148 = 0.

Answer 1

The equation of the circle is a way to represent the circle in the algebraic equation form.

The general form of the equation of the given circle is,

$x^2+y^2+6x-24y+128&=0$

Hence, the option C is the correct option.

What is the equation of circle?

The equation of the circle is the equation which is used to represent the circle in the algebraic equation form with the value of center point in the coordinate plane and measure of radius.

The standard form of the equation of the circle can be given as,

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

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

Given information-

The center point of the given circle is $A(-3,12)$.

The radius of the circle is 5 units.

The image of the circle attached below.

To find the equation of the circle, put the value of points and radius in the above form of equation of circle as,

$(x-(-3))^2+(y-12)^2=5^2$

Solve the equation further as,

$\begin{aligned}(x+3)^2+(y-12)^2&=5^2\\x^2+3^2+6x+y^2+12^2-24y&=25\\x^2+y^2+9+144+6x-24y&=25\\x^2+y^2+6x-24y+128&=0\\\end$

Thus the general form of the equation of the given circle is,

$x^2+y^2+6x-24y+128&=0$

Hence, the option C is the correct option.

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