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प्रश्न
Given equation of line L1 is y = 4.
(i) Write the slope of line, if L2 is the bisector of angle O.
(ii) Write the coordinates of point P.
(iii) Find the equation of L2
उत्तर
Equation of L1 is y = 4 (given)
(i) As L2 is bisector of O
⇒ L2 is inclined at an angle of 45° with XX'
∴ Slope of L2 = m = tan 45° = 1
(ii) Slope of L2 = `(4 - 0)/(x - 0)`
⇒ 1 = `(4)/x`
⇒ x = 4
So coordinates of P are (4, 4).
(Since the slope of L2 is 1, L2 ⇒ PM = OM)
(iii) L2 passes through O(0, 0), P(4, 4) and has slope m = 1
∴ Equation of L2 is
y - y1 = m (x - x1)
y - 0 = 1 (x - 0)
or y = x
or x - y = 0.
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