Chapter 11.2, Problem 25SR

(a)

To determine

To find: The point(s) of intersection of the orbits of Pluto and the comet.

Answer to Problem 25SR

The point(s) of intersection of the orbits of Pluto and the comet are $\left(39.24,4.386\right)$ and $\left(39.24,-4.386\right)$ .

Explanation of Solution

Given:

The given equation of orbit of Pluto and the comet is given as:

  $\begin{array}{c}\frac{x^2}{{39.5}^2}+\frac{y^2}{{38.3}^2}=1\\ x=y^2+20\end{array}$

Calculation:

The graph of the above functions is given as:

  

The point(s) of intersection of the orbits of Pluto and the comet by using the graph is given as:

  $\left(39.24,4.386\right)$ and $\left(39.24,-4.386\right)$ .

(b)

To determine

To find: The comet will always hit the Pluto.

Answer to Problem 25SR

No, the comet will not always hit the Pluto.

Explanation of Solution

From the graph shown below, it is clear that if the vertex of the parabola will be taken $\left(45,0\right)$ the comet will not hit the Pluto.

  

(c)

To determine

To find: The intersection point of given two graphs.

Answer to Problem 25SR

The intersection points are $\left(1,3\right)$ and $\left(-1.667,-2.333\right)$ .

Explanation of Solution

Given:

The given equations are given as:

  $\begin{array}{c}y=2x+1\\ 2x^2+y^2=11\end{array}$

Calculation:

From the graph shown below the intersection points are $\left(1,3\right)$ and $\left(-1.667,-2.333\right)$ .

  

(d)

To determine

To find: The intersection point of given two graphs.

Answer to Problem 25SR

The intersection points are $\left(3,4\right);\left(-3,4\right);\left(3,-4\right);\left(-3,-4\right)$ .

Explanation of Solution

Given:

The given equations are given as:

  $\begin{array}{c}2x^2+3y^2=66\\ x^2+y^2=25\end{array}$

Calculation:

From the graph shown below the intersection points are $\left(3,4\right);\left(-3,4\right);\left(3,-4\right);\left(-3,-4\right)$ .