### Home > CALC > Chapter 7 > Lesson 7.1.4 > Problem7-44

7-44.

Find the equation of the line(s) tangent to $y = x^2 + 2x + 4$ that pass through the origin. .

$y = x^2 + 2x + 4$ has infinitely many tangent lines; two of them go through the origin.

Let the point of tangency be (a, y(a)) or (a, (a2 +2a + 4)).

Therefore, the slope of the tangent lines must be $y^\prime(a) = 2a + 2$.
Of course, we do not know the value of '$a$' yet.

Write the equation of the tangent line(s) using Point-Slope form. Then solve for $y$. We will solve for '$a$' next.

Since we know that the lines pass through the origin, evaluate ($x, y$) for ($0,0$). This will give you the values of '$a$'.

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