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Find the shortest distance from the point (0,8) to the parabola x

2
−4y=0. (Give an exact answer. Use symbolic notation and fractions where needed.)

1 Answer

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Final answer:

The shortest distance is 8 units. To find the shortest distance from the point (0,8) to the parabola x^2 - 4y = 0, we need to find the point on the parabola that is closest to the given point.

Step-by-step explanation:

To find the shortest distance from the point (0,8) to the parabola x2 - 4y = 0, we need to find the point on the parabola that is closest to the given point. We can do this by finding the coordinates of the vertex of the parabola. The equation of the parabola is in the form y = ax + bx2, so we can rewrite it as 4y = x2. Rearranging the equation, we get y = (1/4)x2. Since the parabola opens upward, the vertex is the minimum point on the parabola, which occurs at the axis of symmetry x = 0.

Therefore, the vertex of the parabola is (0,0). The shortest distance from the point (0,8) to the parabola is the line segment connecting the point (0,8) to the vertex (0,0). We can find the length of this line segment using the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2). Plugging in the values, we get d = sqrt((0 - 0)^2 + (8 - 0)^2) = sqrt(0 + 64) = sqrt(64) = 8.

User Dima Malenko
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