What is a counterexample to this claim?
1 answer:
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For this, I'll be using the substitution method. Since y = 1/3x - 6, replace the y variable in the first equation with 1/3x - 6 and solve for x:
Now that we have the value of x, plug it into either equation to solve for y:
Answer:
The equation for the circle is:
Step-by-step explanation:
Here, let us assume the two end points of the diameter are:
P (3,-1) and Q (-2,-1)
Now, as we knew diameter is the chord that passer through the center of the circle.
⇒ Mid point of DIAMETER = Center coordinates of the Circle
Let us assume O(x,y) is the center of the line segment PQ.
So, by MID POINT FORMULA:
⇒ The center coordinates of the circle = O(0.5,-1) ...... (1)
Now, RADIUS = Half of DIAMETER
Using DISTANCE FORMULA:
So, Radius = 5/2 = 2.5 units
Now, the equation of circle with radius r and center coordinate ( h,k) is given as:
Substitute r = 2.5 and (h,k) = (0.5,0) we get:
Hence the equation for the circle is: