Unlocking the Power of ChatGPT and AI in Testing - A Real-World Look, present...
Circle questions
1. QUESTIONS
1- Sketch the circle x2 + y2 = 4.
Find the center and radius first.
-The equation is in the form x2 + y2 = r2, so we
have a circle, center (0, 0) with radius r = √4 = 2
2. 2- Sketch the circle (x − 2)2 + (y − 3)2 = 16
Find the center and radius first.
-The equation is in the form (x − h)2 + (y − k)2 = r2, so we have a
circle with centre at (2, 3) and the radius is r = √16 = 4.
3. 3- Sketch the circle (x + 4)2 + (y − 5)2 = 36
-We have a circle with centre at (-4, 5) and the
radius is r = √36 = 6.
4. 4. Find the equation of the circle with
centre (3/2, -2) and radius 5/2.
-Centre (3/2, -2) radius 5/2
5. 5- Find the points of intersection of the circle
x2 + y2 − x − 3y = 0
with the line
y = x − 1.
-We solve the 2 equations simultaneously by substituting the expression
y = x -1
into the expression
We have:
6. So we see that the solutions for x are x = 1 or x = 2. This gives the
corresponding y-vales of y = 0 and y = 1.
So the points of intersection are at: (1, 0) and (2, 1).
We can see that our answer is correct in a sketch of the situation: