Answer
See graphs
Work Step by Step
1) We are given the ellipse:
$\dfrac{x^2}{16}+\dfrac{y^2}{49}=1$
Determine $h,k,a,b$:
$h=0$
$k=0$
$a^2=49\Rightarrow a=\sqrt{49}=7$
$b^2=16\Rightarrow b=\sqrt{16}=4$
The centre is $(h,k)=(0,0)$ and the endpoints $(0,-7),(0,7),(-4,0),(4,0)$.
Graph the ellipse.
2) We are given the ellipse:
$\dfrac{x^2}{49}+\dfrac{y^2}{81}=1$
Determine $h,k,a,b$:
$h=0$
$k=0$
$a^2=81\Rightarrow a=\sqrt{81}=9$
$b^2=49\Rightarrow b=\sqrt{49}=7$
The centre is $(h,k)=(0,0)$ and the endpoints $(0,-9),(0,9),(-7,0),(7,0)$.
Graph the ellipse.
3) We are given the ellipse:
$y^2=1-4x^2$
$4x^2+y^2=1$
$\dfrac{x^2}{\dfrac{1}{4}}+\dfrac{y^2}{1}=1$
Determine $h,k,a,b$:
$h=0$
$k=0$
$a^2=1\Rightarrow a=\sqrt{1}=1$
$b^2=\dfrac{1}{4}\Rightarrow b=\sqrt{\dfrac{1}{4}}=\dfrac{1}{2}$
The centre is $(h,k)=(0,0)$ and the endpoints $(0,-1),(0,1),\left(-\dfrac{1}{2},0\right),\left(\dfrac{1}{2},0\right)$.
Graph the ellipse.
4) We are given the ellipse:
$4x^2+25y^2=100$
$\dfrac{4x^2}{100}+\dfrac{25y^2}{100}=1$
$\dfrac{x^2}{25}+\dfrac{y^2}{4}=1$
Determine $h,k,a,b$:
$h=0$
$k=0$
$a^2=25\Rightarrow a=\sqrt{25}=5$
$b^2=4\Rightarrow b=\sqrt{4}=2$
The centre is $(h,k)=(0,0)$ and the endpoints $(-5,0),(5,0),(0,-2),(0,2)$.
Graph the ellipse.
5) We are given the ellipse:
$6x^2=30-5y^2$
$6x^2+5y^2=30$
$\dfrac{6x^2}{30}+\dfrac{5y^2}{30}=1$
$\dfrac{x^2}{5}+\dfrac{y^2}{6}=1$
Determine $h,k,a,b$:
$h=0$
$k=0$
$a^2=6\Rightarrow a=\sqrt 6$
$b^2=5\Rightarrow b=\sqrt 5$
The centre is $(h,k)=(0,0)$ and the endpoints $(0,-\sqrt 6),(0,\sqrt 6),(-\sqrt 5,0),(\sqrt 5,0)$.
Graph the ellipse.
