Question

two lines passing through the point (2,3) intersects each other at an angle of 60°, If slope of one line is 2, find equation of the other line

Answer 1

Given point of intersection is (2,3) and the angle between the line is 60∘60∘Also m1=2m1=2∴tanθ=∣∣∣m1−m21+m1m2∣∣∴tan⁡θ=|m1−m21+m1m2|Substituting the values we get,tan60∘=∣∣∣2−m21+2m2∣∣tan⁡60∘=|2−m21+2m2|But tan60∘=3–√tan⁡60∘=33–√=±(2−m2)1+2m23=±(2−m2)1+2m2On rearranging we get,3–√(1+2m2)=±(2−m2)3(1+2m2)=±(2−m2)Taking the positive value we get,3–√(1+2m2)=2−m23(1+2m2)=2−m2⇒m2(23–√+1)=2−3–√⇒m2(23+1)=2−3⇒m2=2−3–√23–√+1⇒m2=2−323+1Taking the negative value3–√(1+2m2)=−(2−m2)3(1+2m2)=−(2−m2)m2(23–√−1)=−2−3–√m2(23−1)=−2−3⇒m2=−(2+3–√)23–√−1