 Hi and welcome to the session. Let us discuss the following question. The question says two lines passing through the point 2, 3 intersects each other at an angle of 60 degree. If the slope of one line is 2, find the equation of the other line. Let's now begin with this solution. In this question, we are given the angle between two lines and slope of one line. Now using the formula for angle between two lines, we will find the slope of other line and after that we will find the required equation of other line. So slope of one line is 2, slope of other line be m. We know that angle between two lines whose slopes are m1 and m2 is given by tan theta is equal to mod of m2 minus m1 upon 1 plus m1 into m2. Now here theta is equal to 60 degree and slope of one line is 2 and other line is m. So now substitute the values in this formula. By substituting the values we get tan 60 degree is equal to mod of m minus 2 upon 1 plus 2 m. Now this implies rule 3 is equal to plus minus m minus 2 upon 1 plus 2 m. Now first of all, consider 3 is equal to m minus 2 upon 1 plus 2 m. Now this implies root 3 plus 2 root 3 m is equal to m minus 2. This implies 2 root 3 m minus m is equal to minus 2 minus root 3. This implies 2 root 3 minus 1 into m is equal to minus 1 into 2 plus root 3. This implies m is equal to minus 1 into 2 plus root 3 upon 2 root 3 minus 1 and this implies m is equal to 2 plus root 3 upon 1 minus 2 root 3. It is also given in the question that both these lines pass through the point 2, 3. So equation of line passing through 2, 3 and having slope m is y minus 3 is equal to 2 plus root 3 upon 1 minus 2 root 3 into x minus 2. This implies y minus 3 into 1 minus 2 root 3 is equal to 2 plus root 3 into x minus 2. This implies y minus 2 root 3 y minus 3 plus x root 3 is equal to 2 x minus 4 plus root 3 x minus 2 root 3. This implies 2 x minus 4 plus root 3 x minus 2 root 3 minus y plus 2 root 3 y plus 3 minus 6 root 3 is equal to 0. This implies plus root 3 into x plus minus 1 into y minus minus 6 root 3 is minus 8 root 3 minus 4 plus 3 is minus 1 is equal to 0. This implies root 3 plus 2 into x plus 2 root 3 minus 1 into y is equal to 8 root 3 plus 1. So for m is equal to 2 plus root 3 upon 1 minus 2 root 3 equation of other line is root 3 plus 2 into x plus 2 root 3 minus 1 into y is equal to 8 root 3 plus 1 minus root 3 is equal to n minus 2 upon 1 plus 2 n. Now this implies minus root 3 minus 2 root 3 n is equal to n minus 2. This implies minus 2 root 3 n minus n is equal to minus 2 plus root 3. This implies minus 2 root 3 plus 1 into n is equal to minus into 2 minus root 3. And this implies m is equal to 2 minus root 3 upon 2 root 3 plus 1. So equation of passing through and slow minus root 3 upon 1 plus 2 root 3 is y minus 3 is equal to 2 minus root 3 upon 1 plus 2 root 3 into x minus 2. Now this implies y minus 3 into 1 plus 2 root 3 is equal to 2 minus root 3 into x minus 2. This implies y into 1 plus 2 root 3 minus 3 minus 6 root 3 is equal to 2 minus root 3 into x minus 4 plus 2 root 3. This implies 2 minus root 3 into x minus 1 plus 2 root 3 into y minus 4 plus 2 root 3 plus 3 plus 6 root 3 is equal to 0. And this implies root 3 minus 2 into x plus 1 plus 2 root 3 into y is equal to minus 1 plus 8 root 3. So required equation of other line is root 3 minus 2 into x plus 1 plus 2 root 3 into y is equal to minus 1 plus 8 root 3. Hence the required equation of other line are root 3 plus 2 into x plus 2 root 3 minus 1 into y is equal to 8 root 3 plus 1 or root 3 minus 2 into x plus 1 plus 2 root 3 into y is equal to minus 1 plus 8 root 3. This is how required answer. So this completes the session I and take care.