Question

Homer wants to identify the center and radius of the circle defined by the equation x2 + y2 - 14x +

Answer 1

Homer has made mistake in step 2

When you complete the square, you need to add the values to both sides of equation

Solution:

Given equation of circle:

$x^2 + y^2 -14x + 2y -25 = 0$

Let us first calculate center and radius and find out where he did the mistake

Step 1:

Group the terms

$x^2 -14x + y^2 + 2y = 25\\\\(x^2 -14x) + (y^2 + 2y) = 25$

Step 2:

$(x^2 -14x + 49) + (y^2 + 2y + 1) = 25 + 49 + 1$

But homers step 2 is:

$(x^2 -14x + 49) + (y^2 + 2y + 1) = 25$

So homer has made mistake in this step

When you complete the square, you need to add the values to both sides of equation

But homer did not add 49 and 1 to right side of equation

Correct steps are:

$(x^2 -14x + 49) + (y^2 + 2y + 1) = 75\\\\(x-7)^2 + (y+1)^2 = 75$

Comparing general equation of circle,

$(x-h)^2 + (y-k)^2 = r^2$

Therefore, center is ( 7, -1) and radius is 8.66