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December 11th, 2010, 06:25 AM   #1
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verify that the given point is on the curve and find the lin

verify that the given point is on the curve and find the lines that are ( a ) tangent (b) normal to curve at the given point ?

x^2 + xy - y^2 = 1 point ( 2,3)

>>>>

a )

2x +xy'+y-2yy' = 0
y' = -2x - y / x - y

m = y' = -2(2) - 3 / 2-2(3) = 1.75

the Eqation of tangent .. is :
y-3 = 1.75(x-2 )

about (b) how i solve it ?
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December 11th, 2010, 07:41 AM   #2
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Re: verify that the given point is on the curve and find the

You are given the curve and the point (2,3).

To verify that the point is on the curve, make sure

To find the line tangent to the curve at the given point, find y':









Somehow you got the correct slope, but your formula for y' was slightly wrong.

With the slope and the point, we have:



I recommend putting the line into y = mx + b form:



To find the normal line, use the fact that when two slopes are perpendicular, what is their product?
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