 Hi, and welcome to the session. Let's discuss the following question. The question says, if some of the perpendicular distances of a variable point, Pxy from the line x plus y minus 5 is equal to 0 and 3x minus 2y plus 7 is equal to 0 is always 10, show that P must move on a line. Let's now begin with the solution. Let P1 be perpendicular to the distance of point P having coordinates x5 from line x plus 5 minus 5 is equal to 0. The perpendicular distance of point P having coordinates x5 from line x plus 5 minus 5 is equal to 0 is x plus 5 minus 5 upon root 2. And this is equal to P. Now let P2 be perpendicular distance of point P having coordinates x5 from line 3x minus 2y plus 7 is equal to 0. The perpendicular distance of point P having coordinates x5 from line 3x minus 2y plus 7 is equal to 0 is 3x minus 2y plus 7 upon root 30. And this is equal to P2. In a question, it is given that P1 plus P2 is equal to 10. Now substitute the value of P1 and P2 in this equation. Substituting the values, we get x plus 5 minus 5 upon root 2 plus 3x minus 2y plus 7 upon root 30 is equal to 10. And this implies root 30 into x plus 5 minus 5 plus root 2 into 3x minus 2y plus 7 is equal to 10 into square root of 26. And this implies x into root 30 plus 3 root 2 plus y into root 30 minus 2 root 2 minus 5 root 30 plus 7 root 2 minus 10 root 26 is equal to 0. The coordinates of point P, that is x and y, satisfies this equation. So this clearly implies that P is moving on a line. Hence, we have proved that P moves on a line. This completes the session. Bye and take care.