Question

An equation of the circle with centre at (0, 0) and
radius r is

Answer 1

Answer:

x² + y² = r²

Step-by-step explanation:

Given---> Coordinates of centre of circle = ( 0 , 0 )

Radius of circle = r

To find---> Equation of circle

Solution---> ATQ,

Coordinates of centre = ( 0 , 0 )

Radius of circle = r

We know that equation of circle is ,

( x - h )² + ( y - k )² = a² ..............( 1 )

Where coordinates of centre = ( h , k )

Radius of circle = a

So, h = 0 , k = 0 and a = r

Putting h = 0 , k = 0 and a = r in equation ( 1 )

( x - 0 )² + ( y - 0 ) = r²

=> x² + y² = r²

Additional identities--->

1) General equation of circle

x² + y² + 2gx + 2fy + c = 0

Where ,

Coordinates of centre = ( - g , - f )

Radius of circle = √(g² + f² - c )

2) Equation of ellipse is

x² / a² + y² / b² = 1

3) Equation of hyperbola

x² / a² - y² / b² = 1

4) Equation of parabola

y² = 4ax

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