Question 1016146
find the point of intersection of each line to the ellipse {{{x^2/9 + y^2/36 = 1}}}

a.) y=2x+2
{{{x^2/9 + y^2/36 = 1}}}
Sub for y
{{{x^2/9 + (2x+2)^2/36 = 1}}}
{{{4x^2 + 4x^2 + 8x + 4 = 36}}}
{{{8x^2 + 8x - 32 = 0}}}
{{{x^2 + x - 4 = 0}}}
{{{x = -1/2 +sqrt(17)/2}}}
y = 2x + 2
{{{y = 1 + sqrt(17)}}}
--> the point (x,y)
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{{{x = -1/2 -sqrt(17)/2}}}
y = 2x + 2
{{{y = 1 - sqrt(17)}}}
--> the 2nd point (x,y)
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b.) y=-2x-9
Similar to above.
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c.) 2x+5y+3=0
--> y = -(2x + 3)/5
Sub as above.
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If there are no real solutions, there are no intersections.
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