 Hello friends, welcome to the session. I am Malika. Let's discuss the given question. Find the coordinates of a point A where AB is the diameter of the circle, whose center is with the coordinates 2 and minus 3 and B with coordinates 1 and 4. Here is the figure according to the question with AB as the diameter and the coordinates of B are 1 and 4 and that of the center of the circle is 2 and minus 3. Now let's begin with the solution. Now here we have to find the coordinates of A. So let the coordinate AB, so we will write here X and Y. As we all know that the center lies on the midpoint of the diameter of the circle, then according to the problem AB is the diameter and O is the center. So O is the midpoint of diameter AB. So now coordinate given by the midpoint formula that is X1 plus X2 upon 2 and Y1 plus Y2 upon 2. Now we will substitute the value of X1, X2, Y1, Y2 and give the coordinates of O that is here X1 is X plus X2 is 1 upon 2 and Y1 is Y plus Y2 is 4 upon 2. So these are the coordinates of the point O. Now but it is given that the coordinates of O are minus 3 therefore we can say that on equating the corresponding parts we get X plus 1 upon 2 equal to 2 and Y plus 4 upon 2 equal to minus 3. So let this be our first equation and this is our second equation. Now from equation first we have X plus 1 equal to 4. This implies X equal to 3 from equation second that is Y plus 4 upon 2 equal to minus 3. This implies Y plus 4 equal to minus 6. This implies Y equal to minus 6 minus 4. This implies Y equal to minus 10. Therefore coordinates of A will be 3 and minus 10. Therefore 3 and minus 10 are the coordinates of the point A. So hope you understood the solution and enjoyed the session. Goodbye and take care.