# To calculate: The vertices and foci of the conic section: x29 + y24=1 Question
Conic sections To calculate: The vertices and foci of the conic section: $$\displaystyle{x}{29}\ +\ {y}{24}={1}$$ 2021-02-01
Step 1 Formula Used: Eccentricity PSK(e)=1\ -\ b2a2 Step 2 Calculation: Compare the given equation with the equation of an ellipse $$\displaystyle{x}{2}{a}{2}\ +\ {y}{2}{b}{2}={1}$$ and we get: $$\displaystyle{a}{2}={9}\ \Rightarrow\ {a}={3}{b}{2}={4}\ \Rightarrow\ {b}={2}$$ Now, $$\displaystyle{e}={1}\ -\ {b}{2}{a}{2}={1}\ -\ {49}={53}$$ Vertices are: $$\displaystyle{\left(\pm\ {a},\ {0}\right)}\ \text{and}\ {\left({0},\ \pm\ {b}\right)}$$ Now, put the values of a and b to get the vertice of the conic section and we get: $$\displaystyle{\left(\pm\ {a},\ {0}\right)}\ \text{and}\ {\left({0},\ \pm\ {b}\right)}={\left(\pm\ {3},\ {0}\right)}\ \text{and}\ {\left({0},\ \pm\ {2}\right)}$$ Now, $$\displaystyle\text{Foci}\ ={\left(\pm\ {a}{e},\ {0}\right)}={\left(\pm\ {5},\ {0}\right)}$$ Thus, the vertices and foci of the conic section are: $$\displaystyle{\left(\pm\ {3},\ {0}\right)}\ \text{and}\ {\left({0},\ \pm\ {2}\right)}\ \text{and}\ {\left(\pm\ {5},\ {0}\right)}.$$

### Relevant Questions To find the vertices and foci of the conic section: $$\displaystyle{\frac{{{\left({x}\ -\ {4}\right)}^{{{2}}}}}{{{5}^{{{2}}}}}}\ -\ {\frac{{{\left({y}\ +\ {3}\right)}^{{{2}}}}}{{{6}^{{{2}}}}}}={1}$$ To calculate the verties and foci of the conic section: $$\displaystyle{\left({x}{9}\right)}{2}\ +\ {\left({y}{4}\right)}{2}={1}$$ To determine: The conic section and to find the vertices and foci: $$\displaystyle{x}{2}\ -\ {y}{2}{y}={4}$$ Write the equation of each conic section, given the following characteristics:
a) Write the equation of an ellipse with center at (3, 2) and horizontal major axis with length 8. The minor axis is 6 units long.
b) Write the equation of a hyperbola with vertices at (3, 3) and (-3,3). The foci are located at (4, 3) and (-4, 3).
c) Write the equation of a parabola with vertex at (-2,4) and focus at (-4, 4) Write the equation of each conic section, given the following characteristics:
a) Write the equation of an ellipse with center at (3, 2) and horizontal major axis with length 8. The minor axis is 6 units long.
b) Write the equation of a hyperbola with vertices at (3, 3) and (-3, 3). The foci are located at (4, 3) and (-4, 3).
c) Write the equation of a parabola with vertex at (-2, 4) and focus at (-4, 4) Identify the conic section given by $$\displaystyle{y}^{2}+{2}{y}={4}{x}^{2}+{3}$$
Find its $$\frac{\text{vertex}}{\text{vertices}}\ \text{and}\ \frac{\text{focus}}{\text{foci}}$$ Polar equations for conic sections Graph the following conic sections, labeling vertices, foci, directrices, and asymptotes (if they exist). Give the eccentricity of the curve. Use a graphing utility to check your work. $$\displaystyle{r}=\ {\frac{{{10}}}{{{5}\ +\ {2}\ {\cos{\theta}}}}}$$ Find and calculate the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections $$x^2 + 2y^2 - 2x - 4y = -1$$ $$\displaystyle{x}^{2}+{4}{x}+{y}^{2}={12}$$ Find the vertices, foci, directrices, and eccentricity of the curve wich polar conic section Consider the equation $$r^{2} = \sec\ 2\ \theta$$