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Properties of Ellipse

Ellipse: 73359.png
Definition of curve w.r.t. triangle If the base of triangle is given and opposite vertex moves in such a way that sum of two variable side is constant (perimeter of triangle is constant) then locus of moving vertex is ellipse
Position of a point P(hk) with respect to curve
73353.png
P will lie outside, on, or inside the ellipse, 73346.png according as 73340.png
Equation of tangent to curve at point P(x1y1) 73334.png or T = 0
Equation of tangent to curve at point whose eccentric angle is φ 73328.png
Equation of tangent to curve whose slope is m y = mx ± 73322.png
Equation of normal to curve at point P(x1y1) 73316.png
Equation of normal to curve at point whose eccentric angle is φ 73310.png
Points of contact when y = mx + c touches the curve 73304.png
Equation of chord contact w.r.t. any point P(hk) 73298.png
Equation of chord PQ which bisected at point R(hk) 73292.png
Pair of tangents from point P(x1y1) 73286.png
or T2 = SS1
Locus of point of intersection of tangents which are perpendicular or equation of director circle x2 + y2 = a2 + b2
Equation of the chord joining the points P(φ1) and Q(φ2) 73280.png




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