CONIC SECTIONS: PARABOLA,ELLIPSE AND HYPERBOLA (CONT)

THE HYPERBOLA

The hyperbola is the locus of a point P, moving in a plane such that the distance from two fixed points called the foci have a constant difference

GENERAL EVALUATION

1.  Write the equation of the ellipse,  x2 + 3y2 + 2x –24y + 46 = 0 in the canonical form hence determine. Its vertices and foci

2.  Find the vertices and foci of the hyperbola  25x2 – 4y2 = 100

3.  Find the equation of the tangent and normal to the parabola y2 – 18x = 0 at point (2,6)

READING ASSIGNMENT:  New Further Mathematics Project 3 by TuttuhAdegun and Godspower5th  Edition

WEEKEND  ASSIGNMENT

1.  Find the equation of the tangent to the ellipse 4x2 +9 y2 = 36 at point (0,-2)

A, 6y + x = 9   B, 3y + x = 9   C, 6y + 4x = 9  D, y +6 x = -9

2.  Find the foci of the ellipse 4x2 + 9y2 = 72

A, 14 or -14   B,  or –    C, 5 or -5   D,  or –

3.  Find the equation of the normal to the parabola y2-20x = 0 at (3 , 2  )

A. 5y +  x = 13   B. 3y + x = 9  C. 5y + x = 13   D. 5y +  x = 13

4. Which of the  following is true eccentricity of a parabola A.e< 1 B.  e> 1 C. e = 1 D. e >= 1

5. Which of the following is true eccentricity of a hyperbola A. e < 1 B. e > 1 C. e = 1 D. e >=1

THEORY

1.  (a) Show that the points  Q(6 , 2) lies on a circle x+ y2 – 4x +2y -20 = 0  lies on a circle

(b) Find the equation of the tangent to the circle at the point Q

2.  write the equation of the following ellipses in their canonical form and hence determine

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