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Determines the acute angle of intersection of ellipses 4x² + y² - 32x+56= 0 & 6x² + 8y² = 86 at one of their two intersection points

Determines the acute angle of intersection of ellipses 4x² + y² - 32x+56= 0 & 6x² + 8y² = 86 at one of their two intersection points

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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SOLVE STEP BY STEP IN DIGITAL FORMAT PLEASE **** Determines the acute angle of intersection of ellipses 4x² + y²- 32x+56= 0 & 6x² + 8y² = 86 at one of their two intersection points
Transcribed Image Text:SOLVE STEP BY STEP IN DIGITAL FORMAT PLEASE **** Determines the acute angle of intersection of ellipses 4x² + y²- 32x+56= 0 & 6x² + 8y² = 86 at one of their two intersection points
Expert Solution
Step 1: Finding the point of intersection

4x2+y2-32x+56=0      (i)6x2+8y2=86      (ii)

Putting substituting the value of y2  from equation ii we have 

⇒4x2+86-6x28-32x+56=0⇒32x2+86-6x2-256x+448=0⇒                   26x2-256x+534=0⇒                                                 x=8913,3

Only x=3 satisfies the region 

At x=3, y=-2,+2

 

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