SOLUTION: The equation of a curve is y = x^2/(x+2). The tangent to the curve at the point where x = -3 meets the
y- axis at M. The normal to the curve at the point where x = -3 meets the x
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Question 1191708: The equation of a curve is y = x^2/(x+2). The tangent to the curve at the point where x = -3 meets the
y- axis at M. The normal to the curve at the point where x = -3 meets the x - axis at N. Find the
area of the triangle MNO, where O is the origin.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
We first locate the precise point on the curve where the tangent and normal lines are:
So the point we’re looking for is (, ). Next, we find the derivative of the curve, and determine its slope at :
’= ; ->=’
Equation of tangent at is : ; M lie on y-axis, so then the other coordinate of M is
so M( ; - 18)
So the slope of the tangent line is , while the slope of the normal is
Equation of normal at is ; ; the x- coordinate of N is intersection of a line with x-axis
N( ; )
In right triangle : ; ;
then the area is :
square units
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