Question

The standard form of the equation of a circle is (x−4)2+(y−2)2=9.

What is the general form of the equation?
A. x^2+y^2-8x-4y+11=0
B. x^2+y^2+8x+4y-29=0
C. x^2+y^2+8x+4y+11=0
D. x^2+y^2-8x-4y-29=0

Answer 1

A. x^2+y^2-8x-4y+11=0

It is a circle

Answer 2

Option A is correct.

Explanation:

Given equation of circle in standard form is ( x - 4 )² + ( y - 2 )² = 9

We need to find the equation of circle in general form.

To solve the equation in general form we use following identity,

(a - b)² = a² + b² - 2ab

Consider,

( x - 4 )² + ( y - 2 )² = 9

( x² + 4² - 2(x)(4) ) + ( y² + 2² - 2(y)(2) ) = 9

x² + 4² - 8x + y² + 2² - 4y = 9

x² + y² + 16 - 8x + 4 - 4y = 9

x² + y² - 8x - 4y + 16 + 4 - 9 = 0

x² + y² - 8x - 4y + 11 = 0

Therefore, Option A is correct.