goobi
Member
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- Oct 6, 2010
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- HSC
- 2012
Find the equations of the tangent and normal to the ellipse
at the point
.
If the tangent meets the x-axis at P and the normal meets the y-axis at Q, show that PQ touches the ellipse.
Edit:
So I've found the equation of the tangent:
......(1)
And the equation of the normal:
......(2)
Substituting y=0 into (1), P is![](https://latex.codecogs.com/png.latex?\bg_white (2a,0))
Substituting x=0 into (2), Q is![](https://latex.codecogs.com/png.latex?\bg_white (0,\frac{-2a}{\sqrt{3}}))
Gradient of PQ =![](https://latex.codecogs.com/png.latex?\bg_white \frac{1}{\sqrt{3}})
Therefore, equation of PQ is:![](https://latex.codecogs.com/png.latex?\bg_white y=\frac{1}{\sqrt{3}}(x-2a))
And I have no idea what to do next...
Any help would be appreciated![Smile :) :)](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
If the tangent meets the x-axis at P and the normal meets the y-axis at Q, show that PQ touches the ellipse.
Edit:
So I've found the equation of the tangent:
And the equation of the normal:
Substituting y=0 into (1), P is
Substituting x=0 into (2), Q is
Gradient of PQ =
Therefore, equation of PQ is:
And I have no idea what to do next...
Any help would be appreciated
Last edited: