CONIC SECTIONS: PARABOLA,ELLIPSE AND HYPERBOLA (CONT)

THE ELLIPSE

An ellipse is the locus of a point P, moving in a plane such that the sum of its distances from two fixed points F1 and Fcalled the foci, is a constant.

Example: find the equation of the tangent and normal to the ellipse 4x2 + 25y2 = 100

Evaluation

1.  Find the foci and vertices of the following ellipses

(a) 9x2 + 10y2 = 90 (b) 4y2 + 5x2 = 20

2.  Write the equation of the ellipse, 4x2 + 5y2 – 24x – 20y + 36 = 0 in the canonical form hence determine

Its vertices and foci

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