Answer:
Step-by-step explanation:
Let the function be:
f(x, y) = 2(y^2) - x^2 = 8
Since the shortest distance is basically a straight line from point (3, 0) to
f(3, y).
2y^2 - 3^2 = 8
2y^2 = 17
y = sqrt(17/2)
So the nearest point on the planes course to the point (3,0) is (3, sqrt(17/2))
Now lets use the distance formula:
x1 = 3
y1 = 0
x2 = 3
y2 = sqrt(17/2)
[tex]=\sqrt{\left(3-3\right)^2+\left(\sqrt{\frac{17}{2}}-0\right)^2}[/tex]
[tex]=\sqrt{(0)^2+(\sqrt{\frac{17}{2}})^2}[/tex]
[tex]=\sqrt{(\sqrt{\frac{17}{2}})^2}[/tex]
[tex]=\sqrt{\frac{17}{2} }[/tex]
So m in this case is just 17/2 and the square root of m is sqrt(17/2) = 2.91547594742
