Question

the coordinates of the centre of the circle 2x^2+2y^2+ax+by+c=0 are (3,-4);find a and b​

Answer 1

Answer:

a=-6 and b=8

Step-by-step explanation:

2x²+2y²+ax+by+c=0

Or x²+y²+ax/2+by/2+c/2=0

(x²+ax/2)+(y²+by/2)=-c/2

adding a²/4+b²/4 both sides

(x²+ax/2+a²/4)+(y²+by/2+b²/4)= -c/2+a²/4+b²/4

(x+ a/2)² +( y+b/2)² =  a²/4+b²/4-c/2..............(1)

This equation becomes in the form

(x-h)²+(y-k)² =l...........................(2)

Then centre of circle is ( h,k)

Given centre is ( 3,-4)

so eqn is :

(x-3)²+(y+4)²=l.....................(3)

On cmparing (1) and (3) we get

a/2=-3 , a=-6

b/2=4, b=8

Answer 2

Answer:

a = -6

b = 8

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