Question

Equation of normal which is equally inclined with the coordinate axes

Answer 1

Solution:

From the above diagram it is clear that; there are two lines PQ and RS, equally inclined to the co-ordinate axes.

For line PQ: m = tan 45° = 1

and (x11, y11) = (-2, 3)

Therefore, its equation: y – y11 = m(x – x11)

⟹ y – 3 = 1(x + 2)

⟹ y - 3 = x + 2

⟹ y = x + 5

For line RS: m = tan (-45°) = -1

and (x11, y11) = (-2, 3)

Therefore, its equation: y – y11 = m(x – x11)

⟹ y – 3 = -1(x + 2)

⟹ y - 3 = -x - 2

⟹ y = -x + 1

Therefore, the required equations are y = x + 5 and y = -x + 1