Sure, let's solve this step by step.

Step 1: Find the midpoint of the two points (2,3) and (5,7). This will be the center of the circle.

The midpoint formula is ((x1+x2)/2, (y1+y2)/2).

So, the midpoint is ((2+5)/2, (3+7)/2) = (7/2, 10/2) = (3.5, 5).

Step 2: The center of the circle lies on the line 4x-3y=1. So, substitute the coordinates of the center into the equation of the line.

4(3.5) - 3(5) = 1
14 - 15 = 1
-1 = 1

This is not possible, so there is no circle that passes through the points (2,3) and (5,7) with its center on the line 4x-3y=1.

Question

Sure, let's solve this step by step.

Step 1: Find the midpoint of the two points (2,3) and (5,7). This will be the center of the circle.

The midpoint formula is ((x1+x2)/2, (y1+y2)/2).

So, the midpoint is ((2+5)/2, (3+7)/2) = (7/2, 10/2) = (3.5, 5).

Step 2: The center of the circle lies on the line 4x-3y=1. So, substitute the coordinates of the center into the equation of the line.

4(3.5) - 3(5) = 1
14 - 15 = 1
-1 = 1

This is not possible, so there is no circle that passes through the points (2,3) and (5,7) with its center on the line 4x-3y=1.

Knowee AI · Accepted Answer

Sure, let's solve this step by step.

Step 1: Find the midpoint of the two points (2,3) and (5,7). This will be the center of the circle.

The midpoint formula is ((x1+x2)/2, (y1+y2)/2).

So, the midpoint is ((2+5)/2, (3+7)/2) = (7/2, 10/2) = (3.5, 5).

Step 2: The center of the circle lies on the line 4x-3y=1. So, substitute the coordinates of the center into the equation of the line.

4(3.5) - 3(5) = 1
14 - 15 = 1
-1 = 1

This is not possible, so there is no circle that passes through the points (2,3) and (5,7) with its center on the line 4x-3y=1.

Find the the general equation of the circle in the plane that passes through the points (2,3) and (5,7) in such a way that its centre is on the line 4x-3y=1.