Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

    
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

774,904 users

Write 2x^2+2y^2-16x-8y+8=0 in the standard form

0 votes

write the equation in standard form

asked Dec 2, 2013 in ALGEBRA 2 by mathgirl Apprentice

2 Answers

0 votes

2x^2+2y^2-16x-8y+8 = 0

Divide to each side by 2.

(2x^2+2y^2-16x-8y+8)/2  = 0/2

x^2+y^2-8x-4y+4 = 0

Compare it to circle equation form x^2+y^2+2gx+2fy+c = 0

Here centere is (-g,-f)

r = sqrt (g^2+f^2-c)

Given circle centere is (4,2) and radious is 4.

Standard form is x^2+y^2-8x-4y+4 = 0.

 

answered Dec 2, 2013 by william Mentor

x 2 +y 2+ 2gx + 2fy + c = 0 is general equation of a circle.

Standard form of a circle equation is image.

0 votes

The equation is 2x 2 + 2y 2 - 16x - 8y + 8 = 0

Here x 2 coefficient is 2 , for perfect square make x 2 and y 2coefficient 1 by dividing each side by 2.

x 2 + y 2 - 8x - 4y  = -4

To change the expression into a perfect square  add (half the x coefficient)² and add (half the y coefficient)²to each side of the expression.

Here x coefficient = -8. so, (half the x coefficient)² = (-8/2)2= 16

Here y coefficient = 4. so, (half the y coefficient)² = (4/2)2= 4

Add 16 and 4 to each side

x 2 - 8x +16 + y - 4y + 4 = - 4 +16 + 4

(x - 4)2 + (y - 2)2 = 16

(x - 4)2 + (y - 2)2 = 42

Compare it to standard form of a circle equation is image

Where center is (h ,k ) and radius of circle is r .

Radius of circle r = 4 and center of the circle is (4, 2).

Standard form of 2x 2 + 2y 2 - 16x - 8y + 8 = 0 is (x - 4)2 + (y - 2)2 = 42 .

 

answered May 24, 2014 by david Expert

Related questions

...