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| Math Central | Quandaries & Queries |
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Question from Reuchen, a student: Find equations of the lines tangent to y^2=4x and containing (-2,1). |
Hi Reuchen,
Suppose that $P$ is a point on the curve where the tangent line to the curve at $P$ passes through $(-2, 1).$ Let $P$ have coordinates $(a, b)$ then since $P$ is on the curve we know that $b^2 = 4a.$
- Find the slope of the line containing $P = (a, b)$ and $(-2, 1).$
- Differentiate both sides of $y^2 = 4 x$ with respect to $x$ and solve for $y'.$ Evaluate $y'$ at $P.$
The value of $y'$ at $P$ and the slope you found in part 1. are both the slope of the tangent line to the curve at $P.$ Substitute for $a$ using $b^2 = 4a$ and solve for b.
Penny
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