1. Problem 50
Find the shortest distance from the point (4, 2) to the ellipse x2 + 3y2 = 12.
Solution:
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from
By trial and error

2. The nearest point is (3, 1)
Nearest distance:
answer
→ slope of tangent at any point
Thus, slope of normal at any point is
Equation of normal:
the same equation as above (okay)
Problem 51
Find the shortest distance from the point (1 + n, 0) to the curve y = xn, n > 0.
Solution:
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3. by inspection: x = 1
1 raise to any positive number is 1
answer
slope of tangent at any point
Thus, slope of normal at any point is
Equation of normal:
By trial and error

4. Nearest point on the curve is (3, 3)
Shortest distance
answer