# Find the equation of the circle

• zorro
In summary, the equation of the circle that touches the axes and has a center on the line x-2y=3 can only be of the form (a,a) or (a,-a). The line y=x/2-3/2 does not intersect with the lines y=x and y=-x, so a circle with its center on this line cannot exist.
zorro

## Homework Statement

Find the equation of the circle which touches the axes and whose centre lies on the line x-2y=3

## The Attempt at a Solution

The given line passes through 1st, 3rd and 4th quadrants.
So the centre of the circle may lie in any of these i.e. it can be of the form (a,a) (a,-a) (-a,-a).
But my book considers only (a,a) (a,-a) for finding the equation of circles.

for the line $$y=x/2-3/2$$ even though it passes through the first quadrant, it doesn't intersect the line y=x, x>0 so there cannot exist a circle with centre on that line which touches both x and y axes.

Thanks alot!

No problem You don't even have to consider which quadrants the line is in, just start solving for that line and the lines y=x and y=-x.

## 1. What is the formula for finding the equation of a circle?

The formula for finding the equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center point of the circle and r is the radius.

## 2. How do I find the center and radius of a circle given three points on the circle?

To find the center and radius of a circle given three points on the circle, you can use the formula (x1 + x2 + x3)/3 = h and (y1 + y2 + y3)/3 = k to find the center point (h,k). Then, you can use the distance formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2) to find the radius.

## 3. Can I use the Pythagorean theorem to find the equation of a circle?

No, the Pythagorean theorem is used to find the length of the sides of a right triangle, not the equation of a circle.

## 4. How many points are needed to determine the equation of a circle?

At least three points are needed to determine the equation of a circle. However, more points can be used to ensure accuracy and to check for consistency.

## 5. What is the difference between the standard form and general form of the equation of a circle?

The standard form of the equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center point and r is the radius. The general form, on the other hand, is x^2 + y^2 + Dx + Ey + F = 0, where D, E, and F are constants. The standard form is easier to use for graphing and finding the center and radius, while the general form is useful for finding the equation of a circle when given other information such as the diameter or points on the circle.

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