Sketch the ellipse using the latera recta
Answer to Problem 61E
The end points of the two latera recta are
Graph is shown below.
Explanation of Solution
Given:
To sketch the graph of the following ellipse using laterarecta:
Rearranging the above equation
First find out the later are cta.
The Lat us rectumis a line segment through a focuso fanel lipse with end point son the ellipse and perpendicular to the majorax is.
Thus,find the foci of the ellipse.
Thestandardequationofanellipsewithmajoraxisverticalis
Comparing this with equation(1)
Thus,the center of the ellipseis(0,0)
Also,
Next,
The focilion the points
Thus,the fociar eat
This tells that the two laterarectalie on the lines
To find out the inter section points of the two lines with the ellipse.
Substituting
.
Thus,the end points of the two laterarect a are
Thus,the graph of the ellipse can be drawn as below:
The two rectaared epicted in the graph and the ir end-points marked.
Chapter 10 Solutions
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