Answer:
The locus of the coordinates given is a straight line having equation 3x + 2y = 15.
Step-by-step explanation:
Let at any particular value of t, the coordinates of the point are (h,k).
So, h = 2t + 3
⇒ 2t = h - 3
⇒ [tex]t = \frac{h - 3}{2}[/tex]
Again, k = - 3t + 3
⇒ 3t = 3 - k
⇒ [tex]t = \frac{3 - k}{3}[/tex]
Therefore, eliminating t we get a relation between h and k.
Hence, [tex]\frac{h - 3}{2} = \frac{3 - k}{3}[/tex]
⇒ 3h - 9 = 6 - 2k
⇒ 3h + 2k = 15
Therefore, converting in to current coordinates we get the locus of the point (h,k) as 3x + 2y = 15, which is a straight line.
For this reason, the resulting graph is a line and its equation is 3x + 2y = 15. (Answer)
