Find the coordinates of the center of the circle x^2 +y^2 -4x+ 6x =12, and the ones of the conic section?

Question

x^2+64y = 0

Sorry , I intended '+6y' in lieu of '6x ' !
Spelling error !

Answer 1

The general equation of a circle is :-
ax^2 + by^2 + 2gx + 2fy + c=0 where a= coefficient of x^2
b=coeff. of y^2 , c= constant. and the center of the circle is given by:- (-g, -f)

As for ur problem lets first convert ur equation in standard form.
thus ur equation can now be written as:-

1*(x^2) + 1*(y^2) + 2*(-2)x + 2*(3)y - 12=0

Where :- the sign ' * ' means multiplication
a= 1 , b=1 , g=-2 ,f=3 & c= -12

Hence center of circle is (-g ,-f)= (2 , -3)



the radius is given by the formula :-
under-root of g^2 + f^2 - c

thus radius of ur eqn. is :-
under root of (-2)^2 + 3^2 - (-12) = under root 4 + 9 + 12 = under root 25 = 5

hope u understood the method in case of any queries or problems contact me at my e-mail id.

Bye Take Care :-)

Answer 2

equation given;
x^2 +y^2 -4x+ 6y =12
now,
(x-2)^2+(y+3)^2
=x^2+y^2-4x+6y
+(-2)^2+(3)^2
=x^2+y^2-4x+6y+13
hence,
x^2 +y^2 -4x+ 6y =
(x-2)^2+(y+3)^2-13=12
(x-2)^2+(y+3)^2=25
this is the standard circle
equation;
(x-p)^2+(y-q)^2=r^2
where r is the radius,
p and q are the co-ordinates
of the centre of the circle
this gives centre O(2,-3)
and radius 5
as regards x^2+64y = 0,
this is the equation of an
inverted parabola

i hope that this helps

Answer 3

I think you have a typo. Your equation should say
x^2 + y^2 -4x +6y = 12.
The solution is then as follows:
Looking at the coefficients of x and y, we can re-write the equation as :
[(x-2)^2 -4]+ [(y+3)^2 -9] =12
i.e. (x-2)^2 + (y+3)^2 +1 = 0

This gives a circle of radius 1, with a centre at (2,-3)

Answer 4

Co-ordinates of circle :-
'-4x' change the sign and divide by 2, so
'-4x' becomes
'+4x'
' 2' - > the 'x' component.
'+6y' change the sign and divide by 2, so
'+6y' becomes
'-6y'
'-3' -> the 'y' component.
So co-ordinates are (2,-3).

Answer 5

You ahve written -4x + 6x
Is that correct?
If it is, then:
x^2+2x + y^2 = 12
Completing the squae gives
(X +1)^2 + y^2 = 10
Centre of cirlce at (-1,0) and radius sqrt(10)

Answer 6

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Answer 7

math homework?
(2,-3)