Lisandro is using this diagram to find the equation of a circle. He notices that the radius, the blue line, and the red line form a right triangle. Which shows his correct reasoning and equation

a) The length of the red line is |x + h|.
The length of the blue line is |y + k|.
The equation of a circle is (x + h)2 + (y + k)2 = r2.

b) The length of the radius is r.
The area of a circle is πr2.
The equation of the circle is y = πr2x.

c) The length of the red line is |x – h|.
The length of the blue line is |y – k|.
The equation of a circle is (x – h)2 + (y – k)2 = r2.

d) The length of the red line is |x – h|.
The length of the blue line is |y – k|.
The equation of a circle is (x – h)2 + (y – k)2 = r.

The length of the red line is |x – h|. The length of the blue line is |y – k|. The equation of the circle will be (x-h)²+(y-k)²=r².

What is the equation of a circle?

The equation of a circle is given by the general equation,

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where (h,k) are the coordinates of the centre of the circle, and r is the radius of the circle.

As it is given that the blue line and the red line are the radii of the circle, therefore, they will be joining any point on the circle to the centre of the circle.

Given that the blue line is represented by |y+k| while the red line is represented by |x+h|, therefore, the coordinate of the centre of the circle will be (h,k). And the radius of the circle will be r. Thus, the equation of the circle will be (x-h)²+(y-k)²=r².

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