2. (a) Given the point (2, 1) in the (x, y) plane and the line 3r + 2y = 4, find the distance from the point to the line by using the method of Chapter 3, Section 5. (b) Solve part (a) by writing a formula for the distance from (2, 1) to (x, y) and minimizing the distance (use Lagrange multipliers). (c) Derive the formula axo + byo – c D = Va? + b² for the distance from (xo, yo) to ax +by = c by the methods suggested in parts (a) and (b).

Question
2.
(a)
Given the point (2, 1) in the (x, y) plane and the line 3r + 2y = 4, find the
distance from the point to the line by using the method of Chapter 3, Section 5.
(b)
Solve part (a) by writing a formula for the distance from (2, 1) to (x, y) and
minimizing the distance (use Lagrange multipliers).
(c)
Derive the formula
axo + byo – c
D =
Va? + b²
for the distance from (xo, yo) to ax +by = c by the methods suggested in parts
(a) and (b).
Expand
Transcribed Image Text

2. (a) Given the point (2, 1) in the (x, y) plane and the line 3r + 2y = 4, find the distance from the point to the line by using the method of Chapter 3, Section 5. (b) Solve part (a) by writing a formula for the distance from (2, 1) to (x, y) and minimizing the distance (use Lagrange multipliers). (c) Derive the formula axo + byo – c D = Va? + b² for the distance from (xo, yo) to ax +by = c by the methods suggested in parts (a) and (b).

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