Question

find the equation of the circle passing through (3,4) and having the center at (-3,4)​

Answer 1

Step-by-step explanation:

GIVEN : -

The equation of the circle passing through ( 3 , 4 ) having the center at ( -3 , 4 ).

TO FIND : -

The equation of the circle for the given data.

SOLUTION : -

We know that ,

$Equation \: of \: a \: circle \: \\ = {(x - x0)}^{2} + {(y - y0)}^{2} = {r}^{2}$

Where, ( x0 , y0 ) are the co-ordinates of center of the circle and r is radius.

To find the radius of the circle ,

$r \: = \sqrt{ {(x0 - x1)}^{2} + {(y0 - y1)}^{2} } \\ \\ r \: = \sqrt{ {(3 - ( - 3))}^{2} + {(4 - 4)}^{2} } \\ \\ r \: = \sqrt{ {3}^{2} } = \sqrt{9} \\ \\ r \: = 3$

Hence , the equation of a circle is ,

==> ( x - (-3))² + ( y - 4 )² = ( 3 )²

==> ( x + 3 )² + ( y - 4 )² = 9