Answer:
(x-9)^2 + (y-9)^2 = 81
Step-by-step explanation:
Step-by-step explanation:Equation of a circle
( x - h )^2 + ( y - k )^2 = r^2
Your graph - the circle intersects the x-axis at (9 , -9)
- the circle intersects the y-axis at (9 , -9)
h = the number on the x axis intersected by the circle.
k = the number on the y axis intersected by the circle.
r = radius of the circle measured starting from the origin.
plug these in:
( x - h )^2 + ( y - k )^2 = r^2.
(x - 9)^2 + (y - 9)^2 = 9^2
(x-9)^2 + (y-9)^2 = 81
We are given with a circle and we need to find the equation of the circle , but first let's recall that , the equation of a circle with radius 'r' and centre at (h,k) is given by [tex]{\bf{(x-h)^{2}+(y-k)^{2}=r^{2}}}[/tex]
Now , here as as the circle cuts the +ve x-axis at (9,0) . So , it's radius is 9 units or the 2nd way is to measure the distance from centre of the circle to the point where the circle cuts the graph , as the centre is at Origin , so here (h,k) = (0,0) .Which means that the centre is located at the point whose coordinates are (0,0) which is also known as origin . Now , finding the equation of the circle :-
[tex]{:\implies \quad \sf (x-0)^{2}+(y-0)^{2}=(9)^{2}}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{x^{2}+y^{2}=81}}}[/tex]
This is the required equation of Circle