Question

In the xy-plane, the graph of 2x2−6x+2y2+2y=45 is a circle? What is the radius of the circle?

Answer 1

Answer:

Radius = 5

Step-by-step explanation:

The standard form of the  equation of a circle  = ( x-a )²+( y- b)² = r²

where (a ,b) are the coordinates of the centre and r is the radius.

Dividing all the terms by 2, hence

= x²-3x+y²+y= 45/2

Using the completing square method -

= x²-3x+9/4y²+y+1/4= 45/2+9/4+1/4

= (x-3/2)²+(y+1/2)²

= 25

r² = 25

r = 5

Thus, the radius of circle is 5

Answer 2

Answer:

Radius is 5 units

Step-by-step explanation:

Concept used:

General equation of circle is

$x^2+y^2+2gx+2fy+c=0$

Its radius

$r=\sqrt{g^2+f^2-c}$

Given:

$2x^2+2y^2-6x+2y-45=0$

Divide both sides by 2 we get

$x^2+y^2-3x+y-\frac{45}{2}=0$

This equation is of the form

$x^2+y^2+2gx+2fy+c=0$

Hence the given equation represents a circle.

Here,

$g=\frac{-3}{2},\:f=\frac{1}{2},\:c=\frac{-45}{2}$

Radius:

$r=\sqrt{g^2+f^2-c}$

$r=\sqrt{(\frac{-3}{2})^2+(\frac{1}{2})^2-(\frac{-45}{2})}$

$r=\sqrt{\frac{9}{4}+\frac{1}{4}+\frac{45}{2}}$

$r=\sqrt{\frac{9+1+90}{4}}$

$r=\sqrt{\frac{100}{4}}$

$r=\sqrt{25}$

$r=5$ units