Question

Which of the following is an equation of the circle with a center at (-1,4) and a radius of 2√5 units? plss pahelp naman

A. x²+ y²+2x-8y-3=0

B. x²+y²-2x-8y+3=0

C. x²+y²+2x+8y-3=0

D. x²+y²-2x+8y+3=0​

Answer 1

Option A

Explanation:

The standard form of an equation of a circle is represented by the formula
`(x-h)^2+(y-k)^2 = r^2`. Remember that
`(h,k)` is the center and
`r^2` is the radius squared.

So, the equation of the circle must be
`(x+1)^2 +(y-4)^2 = 20`. Complete the square to change the form of the equations listed in the options and find the one that is equal.

Let's try this with option A. Move the constants to the right side, then use the completing the square method to place the equation in standard form:

`x^2 + y^2 +2x -8y -3 = 0\\x^2 + y^2 +2x-8y = 3\\x^2 + 2x +y^2-8y = 3\\(x^2 +2x+1)+(y^2-8y +16)=3+1+16\\(x+1)^2 + (y-4)^2=20`

The end result matches with the equation determined before, so option A is the answer.