For each set of functions, indicate its mathematical expression

Question

Could you help me please with the following problem.

For each set of functions, indicate its mathematical expression:

a) parabolas that pass through the origin and the point $(1,1)$

b) circles tangent to the x-axis and whose center is over the line $x = 1$

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Edit

For the parabolas I got $c=0$ and $a+b=1$.

Answer 1

HINT

Start from the general standard equations for

• parabolas: $y=ax^2+bx+c$

• circle: $(x-x_c)^2+(y-y_c)^2=R^2$

and apply the given conditions.

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For the parabolas since we got $c=0$ and $a+b=1$, the general equation is

$$y=ax^2+(1-a)x, \, a \in \mathbb R$$