Question

Find the points on the locus of points that are 7 units from x axis and 3 units from the point (5,1)

Answer 1

The points are on a circle with center (5, 1) and radius 7 units.

Step-by-step explanation:

Given: Find the points on the locus of points that are 7 units from x axis and 3 units from the point (5,1)

Solution:  

The Distance formula is = √(x1 - x2)² + (y1 -y2)²

Now the point is (5, 1) and distance = 3 units.

So 3 = √(x - 5)² + (y - 1)²

Squaring on both sides, we get:

9 =     (x - 5)² + (y - 1)²

A point that is 7 units from x axis, then y co-ordinate is either +7 or -7.

So the equation becomes:

 9 = (x - 5)² + (7 - 1)²

 9 = x² + 25 - 10x + 36

 x² - 10x + 52 = 0

or  

9 = (x - 5)² + (-7 - 1)²

 9 = x² + 25 - 10x + 64

x² - 10x + 70 = 0

Basically the points are on a circle with center (5, 1) and radius 7 units.