Greg hasn’t covered this in the Module 3 videos so why was this question added?
I went through the videos and it was never covered.
Can someone explain the solution to me
What do you need to know?
The equation of a circle in cartesian coordinates with center (a,b) and radius r is usually written as:
(x - a)^2 + (y - b)^2 = r^2
There are other forms (different ways to express a circle), but I don’t think it should be that relevant to you. Maybe one thing that you might need to keep in mind is this isn’t a function (why?)
For a line in cartesian plane, we again have multiple forms (slope intercept, point slope, intercept, …). The most “used” ones are usually the first two i’ve enumerated, but standard form is “superior” in the sense that it can also represent vertical lines (which the first two fail at). Needless to say, what “form” is the best depends on what you want to do with it, but the aforementioned caveat is a good thing to note regardless.
Just like with a line and circle, a quadratic equation can come in many forms (vertex form, standard form, etc.) and each one has its own merits. The most “relevant” (common) one would be the standard form, which is like:
ax^2 + bx + c = 0 which if we want as a function could be equivalently written as f(x) = ax^2 + bx + c.
I guess this is a good primer and for more information u could just google it or something. For your actual question, it’s just applying what is written above.
In particular:
A) Just an equation of a circle with radius k and center (0,0)
B) The standard form of a line is ax + by - c = 0 or alternatively ax + by = c. Clearly a = b = 1 gives you option b, so it matches this “form” and thus is a line.
C) A quadratic function is of the form: y = ax^2 + bx + c. In your question, a = k, b = c = 0 thus it is a parabola.
I think this was briefly covered in the first video or so (in Coordinate Geometry).