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The parabola y = ax²+bx+c passes through the point P(1, 0) and has its vertex at the point V (2, 1). Find the equations of the lines that pass through the point Q(0, 6) and are tangent to the parabola. Determine the points of tangency of these lines.

Respuesta :

Answer:

Step-by-step explanation:

Here's a concise version of the solution:

1. We find the parabola's equation to be y = (1/4)x² - x + 3/4 through the given points and vertex.

2. The slope of the tangent line passing through Q(0, 6) is -1.

3. Using the point-slope form, the tangent line's equation is y = -x + 6.

4. To find the tangency points, solve the system formed by y = (1/4)x² - x + 3/4 and y = -x + 6 (two x-value solutions exist).

5. Substitute the x-values back into the parabola's equation to get the corresponding y-coordinates for the two points of tangency.

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