jdlogo

jdlogo

jdlogo

jdlogo

jdlogo

Home

Locus

The Circle

The Ellipse

The Parabola

The Hyperbola

General Form

Intersections of Lines & Conics

Summary&Test

 

jdsmathnotes

 

 


UNIT 10  : THE CONICS

LESSON 3: THE ELLIPSE HOMEWORK QUESTIONS, PART 1

 

QUICK REVIEW:

Definition:   Given two fixed points in the plane F1 and F2.  An ellipse is the locus (set) of points P such that the sum |PF1+ PF2 |  is a constant.  The two fixed points are the foci.

The centre is the midpoint of the line segment joining the two foci (F1F2).

 

Text Box: Main Ideas: · The sum |PF1+ PF2 | = constant = 2a · A2A1 is the Major Axis and |A2A1| = 2a · B2B1 is the Minor Axis and |B2B1| = 2b · The standard form of the equation of an ellipse, centre (0, 0), foci on the x-axis:is: · The standard form of the equation of an ellipse, centre (0, 0), foci on the y-axis:is: · · The standard form of the equation of an ellipse, centre (h, k), major axis parallel to the x-axis:is: · · The standard form of the equation of an ellipse, centre (h,k), major axis parallel to the y-axis:is: · · · Note a > b always for the ellipse. · For the ellipse the Pythagorean relation a2 = b2 + c2 holds true.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.  The arch of a bridge is in the shape of a semi-ellipse.  If the span of the ellipse (distance between end points of the arch) is 60 m & the height is 10 m,

find the height of the bridge at a point 5 m from the end of the arch.

 

 

 

 

Solutions:

 

   

 

 

 

 

 

 

 

 

 

 

 

 

      

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 Return to top of page

Click here to go to homework questions, part 2

Click here to return to lesson