SOLUTION: Find the equation of the tangent at the point (2,3) to the parabola 3y = x^2 + 5. Also obtain the equation of the line through the point (2,3) perpendicular to this tangent. If the

Algebra ->  Coordinate-system -> SOLUTION: Find the equation of the tangent at the point (2,3) to the parabola 3y = x^2 + 5. Also obtain the equation of the line through the point (2,3) perpendicular to this tangent. If the      Log On


   

Question 1121326: Find the equation of the tangent at the point (2,3) to the parabola 3y = x^2 + 5. Also obtain the equation of the line through the point (2,3) perpendicular to this tangent. If the x axis meet this line an the tangent at A and B respectively. Find the length of AB
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
3y=x%5E2%2B5
y=%281%2F3%29x%5E2%2B5%2F3
dy%2Fdx=%282%2F3%29x


At point (2,3)?
3%2A3=2%5E2%2B5
9=9
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dy%2Fdx=%282%2F3%29%2A2=4%2F3
SLOPE, 4%2F3
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This tangent line at (2,3):
y-3=%284%2F3%29%28x-2%29
y-3=4x%2F3-8%2F3
y=4x%2F3-8%2F3%2B3
y=4x%2F3-8%2F3%2B9%2F3
highlight_green%28y=4x%2F3%2B1%2F3%29

Perpendicular at point (2,3):
y-3=-%283%2F4%29%28x-2%29
y-3=-3x%2F4%2B3%2F2
y=-3x%2F4%2B3%2F2%2B6%2F2
highlight_green%28y=-3x%2F4%2B9%2F2%29

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