Question

Question

Answer 1

Find the slope of the tangent line to the to the elipse

\[ \frac{ x^{2} }{ 4 }+ \frac{ y^{2} }{ 9 } = 1 , point~(1, \frac{ 3\sqrt{3} }{ 2 })\]

Answer 2

Find the slope of the tangent line to the to the elipse

\[\frac{ 1 }{ 4 }\frac{ dy }{ dx } x^{2}+\frac{ 1 }{ 9 }\frac{ dy }{ dx }y^{2} = \frac{ dy }{ dx }1\]

Answer 3

\[2x*\frac{ 1 }{ 4 }+2*\frac{ 1 }{ 9 }y*(\frac{ dy }{ dx }) = 0 \]

\[\frac{ x}{ 2 } +\frac{ 2 }{ 9 }\frac{ dy }{ dx } = 0 \]

\[-(\frac{ x }{ 2 }) = \frac{ 2 }{ 9 }y \frac{ dy }{ dx }\]

\[\frac{ \frac{- x }{ 2 } }{ \frac{ 2 }{ 9 }y } = \frac{ -9x}{ 4y } \]

\[\frac{ -9x }{ 4y } = \frac{ dy }{ dx }\]

\[\frac{ -9(1) }{ 4(\frac{ 3\sqrt{3} }{ 2 }) } = \frac{ -9 }{ 6\sqrt{3} }*\frac{ 6\sqrt{3} }{ 6\sqrt{3} } = \frac{ -54\sqrt{3} }{ 108 } = \frac{ -\sqrt{3} }{ 2 }\]

Answer 4

Just need someone to help verify this.

Answer 5

So i'm assuming that the slope of the line at the Elipse would be

\[y = \frac{ -\sqrt{3} }{ 2}x \]

Answer 6

@imqwerty