SOLUTION: Identify conic section represented by the equation: 4y^2 + 19 + 3x - 16y = 0 Guess = Parabola since it only has one squared Write the equation of the conic section in standard

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Identify conic section represented by the equation: 4y^2 + 19 + 3x - 16y = 0 Guess = Parabola since it only has one squared Write the equation of the conic section in standard      Log On


   

Question 529653: Identify conic section represented by the equation:
4y^2 + 19 + 3x - 16y = 0
Guess = Parabola since it only has one squared
Write the equation of the conic section in standard form:
4y^2 + 19 + 3x - 16y = 0
I got (y-2)^2 = [-3(x+1)]/4. Is that in standard form?
Analytically determine equation of the line that is tangent to conic section at provided point:
(-13, 5)
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Identify conic section represented by the equation:
4y^2 + 19 + 3x - 16y = 0
Guess = Parabola since it only has one squared
It is a parabola.
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Write the equation of the conic section in standard form:
4y^2 + 19 + 3x - 16y = 0
I got (y-2)^2 = [-3(x+1)]/4. Is that in standard form?
Standard form is x = a(y - k)^2 + h
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Starting with (y-2)^2 = [-3(x+1)]/4
4(y-2)^2 = [-3(x+1)]
x%2B1+=+%28-4%2F3%29%28y-2%29%5E2
x+=+%28-4%2F3%29%2A%28y-2%29%5E2+-+1
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Analytically determine equation of the line that is tangent to conic section at provided point:
(-13, 5)
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I don't know what methods you're allowed or expected to use to do this.
I'll differentiate implicitly:
4y^2 + 19 + 3x - 16y = 0
8y*dy + 3dx - 16dy = 0
dy*(8y - 16) = -3dx
y' = dy/dx = -3/(8y - 16)
y'(5) = -1/8
m @ (-13,5) = -1/8