Application of DerivativeHard
Question
If the line ax + by + c = 0 is a normal to the curve xy = 1, then -
Options
A.a, b ∈ R
B.a > 0, b > 0
C.a < 0, b > 0 or a > 0, b < 0
D.a < 0, b < 0
Solution
ax + by + c = 0 is normal to curve
xy = 1
y + x ×
= 0
Normal slope = -
ax + by + c = 0 is a normal
slope =
∴ xy = 1 ∴ x > 0 and y > 0 or x < 0 and y < 0
So
when a > 0, b < 0 and a < 0, b > 0
xy = 1
y + x ×
= 0Normal slope = -
ax + by + c = 0 is a normal
slope =
∴ xy = 1 ∴ x > 0 and y > 0 or x < 0 and y < 0
So
when a > 0, b < 0 and a < 0, b > 0
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