# Area between parabola and a line that don't intersect? 0 or infinity

Mathematics Asked on January 5, 2022

Came across a problem on social media,

Find the area of the region bounded by a parabola, $$y = x^2 + 6$$ and
line a line $$y = 2x + 1$$.

I tried to draw it on paper and they didn’t seem to intersect. So I drew them online (attached screenshot). My answer was 0, but someone said that we assume they meet at infinity and answer would be infinity. Parallel lines don’t diverge like these do, so I think we can assume that they would never interest at infinity.

$$x^2 + 6 = 2x + 1$$ $$x^2 - 2x + 5$$ $$frac{2 pm sqrt{4 - 4(5)}}{2}$$

As you can see by analyzing the discriminant, this quadratic has no real roots, so there are no points at which the two curves intersect. You could say that the area between the curves tends to infinity. As was stated in the comments, whoever posted this most likely intended to include more information/restrictions.

Also, these two curves will not "meet at infinity." Both diverge as $$x$$ gets arbitrarily large

Answered by N. Bar on January 5, 2022

## Related Questions

### Vector field divergence equivalent definition

0  Asked on August 13, 2020 by user_hello1

### Matrix representation of composition of linear transformations

3  Asked on August 12, 2020 by yudop

### Proof of The Third Isomorphism Theorem

1  Asked on August 12, 2020 by abhijeet-vats

### Fast paced but basic introduction to homological algebra

1  Asked on August 11, 2020 by gfr

### Show estimator is consistent

1  Asked on August 8, 2020 by m1996rg

### Counterexample of limsup of sets and measures

0  Asked on August 7, 2020 by david-warren-katz

### mean distance between three point

0  Asked on August 6, 2020 by yaniv765

### Character table of quaternions $Q_8$

1  Asked on August 5, 2020 by roi_saumon

### Evaluate $int frac{2-x^3}{(1+x^3)^{3/2}} dx$

4  Asked on August 5, 2020 by dharmendra-singh

### The minimizers of energy and length of a curve

1  Asked on August 4, 2020 by w-mu

### prove or give counter example, for every holomorphic function on the unit disc there is $f(z)=z$

1  Asked on August 4, 2020 by hash-man

### Is there an easier prime factorization method for the sum of a prime’s powers?

1  Asked on August 3, 2020 by ifn47

### How does the quotient ring $Bbb Z[x]/(x^2-x,4x+2)$ look like?

2  Asked on August 3, 2020 by 2132123

### Calculus of Variations: Looking for theorem that ensures that a given variational problem has maxima and minima

1  Asked on August 3, 2020 by user

### Primality testing using cyclotomic polynomials

1  Asked on August 2, 2020

### Sequence of integers $S_n$ where all elements that $n$ divides increment by one

1  Asked on July 31, 2020 by twentyyears

### Compositeness testing using Jacobi polynomials

1  Asked on July 30, 2020 by pea-terzi

### Branch cut of square root

2  Asked on July 30, 2020

### Nimber multiplication

2  Asked on July 30, 2020 by yberman

### What is the radius of convergence of $a_n$ where $a_{n+1}=frac{n-5}{n+1}a_n$?

2  Asked on July 28, 2020 by lucas