Passing through (2,2√3) and inclined with the x-axis at an angle of 75°
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Answer:
Given that the line is inclined with x-axis at an angle of 75°.
Therefore, slope of line (m)-
m=tan75°
m=tan(45°+30°)
⇒m=
1−tan45°tan30°
tan45°+tan30°
⇒m=
1−1×
3
1
1+
3
1
⇒m=
3
−1
3
+1
Now as we know that the equation of line of slope m passing through (x
1
,y
1
), is give as-
(y−y
1
)=m(x−x
1
)
Therefore equation of line passing through (2,2
3
) and having slope
3
−1
3
+1
is-
(y−2
3
)=
3
−1
3
+1
(x−2)
⇒y(
3
−1)−(6−2
3
)=x(
3
+1)−(2
3
+2)
⇒y(
3
−1)−x(
3
+1)=6−2
3
−2
3
−2
⇒y(
3
−1)−x(
3
+1)=4(1−
3
)
Hence the equation of line passing through the point (2,2
3
) and inclined with the x-axis at an angle of 75° is-
y(
3
−1)−x(
3
+1)=4(1−
3
)
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