Find Equations Of Both Lines Through The Point (2, −3) That Are Tangent To The Parabola Y = X2 + X.
Find the equation of both lines that pass through the point (2, -3) and are tangent to the parabola y = x^2 + x.
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bookB.S. from Mahatma Gandhi University Kottayam, Kerala, India
bookM.S. from University of Kerala , India
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We have to find the equations of both lines through the point (2,-3) that are tangent to the parabola `y=x^2+x`
i.e. `m=y'=2x+1`
Now we find two points on the two tangent lines to y using: `(x,x^2+x)` and (2,-3). This is to show that (x,f(x)) is a point on the original equation f(x).
Now we have to find the slope of these two points and equate it to the derivative or slope of the original equation.
i.e. `2x+1=\frac{x^2+x+3}{x-2}`
i.e. `\mathbf{y=-x-1}`
So the equation of the two tangent lines to the parabola `y=x^2+x` passing through the point (2,-3) are:
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The slope of the line tangent...
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