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Question
Form the differential equation of all the lines which are normal to the line 3x + 2y + 7 = 0.
Solution
Slope of the line 3x - 2y + 7 = 0 is `(- 3)/-2 = 3/2`
∴ slope of normal to this line is `- 2/3`
Then the equation of the normal is
y = `- 2/3 "x" + "k"`, where k is an arbitrary constant.
Differentiating w.r.t. x, we get
`"dy"/"dx" = - 2/3 xx 1 + 0`
∴ `3"dy"/"dx" + 2 = 0`
This is the required D.E.
Notes
The answer in the textbook is incorrect.
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