Ellipse
1.0 Definition
2.0 Standard equation of Ellipse
3.0 Important terms
4.0 Difference between two forms of Ellipse
5.0 Focal Distance of a point
6.0 Parametric Co-ordinates
7.0 Equation of Tangent to Ellipse
7.1 Equation of tangent to a point/Point form
7.2 Parametric form
7.3 Equation of tangent in terms of slope/Slope form
8.0 Equation of Normal to Ellipse
9.0 Pair of tangents
10.0 Chord of contact
11.0 Chord bisected at a given point
12.0 Director circle
8.3 Slope form
The equations of normals of slope $m$ to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ are given by $$y = mx \mp \frac{{m({a^2} - {b^2})}}{{\sqrt {{a^2} + {b^2}{m^2}} }}$$ at the points $( \pm \frac{{{a^2}}}{{\sqrt {{a^2} + {b^2}{m^2}} }}, \pm \frac{{m{b^2}}}{{\sqrt {{a^2} + {b^2}{m^2}} }})$.7.2 Parametric form
7.3 Equation of tangent in terms of slope/Slope form