What is the value of k if the line joining (2,3) and (8, 3) is tangential to y = kx^2 + 6?

Expert Answers

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The line joining the points (2,3) and (8,3) is a horizontal line. y = kx^2 + 6 is a parabola.

If k = 0, the curve y = kx^2 + 6 is a straight line. if k is negative the parabola opens downwards and its highest point is (0, 6). If k is positive the parabola opens upwards and its lowest point is (0, 6). For the line joining (2,3) and (8,3) to be tangential the slope is 0.

y' = 2kx can be 0 only at x = 0 which is at the point (0, 6). The given line does not pass through this point. The line either does not touch the graph of y = kx^2 + 6 or intersects it.

For no value of k can the line joining the points (2, 3) and (8, 3) be tangential to y = kx^2 + 6

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