Question

The circle is tangent to the line 4x+3y = 4 at point (4 , -4) and the center is on x-y = 7. Find the equation of the circle.

Answer 1

calculate the perpendicular distance between line tangent and the center it should work

Answer 2

even i can say that.. plz solve it superhero

Answer 3

lol but i don't wanna do it please dumbcow is here he is good better then me he will figure it out

Answer 4

guys we will scare kris away from open study!!!! plz help him
i am not wanting to solve it coz i am making silly mistakes.. (lol)

Answer 5

haha ok first determine the equation of tangent line in slope-intercept form
\[y=-\frac{4}{3}x +\frac{4}{3}\]
Now the line perpendicular to this line must go through the center of circle.
slope is opposite reciprocal of -4/3
\[m = \frac{3}{4}\]
goes through point (4,-4)
\[-4 = \frac{3}{4}(4) + b\]
\[b = -7\]
Perpendicular line:\[y = \frac{3}{4}x - 7\]
Now we also know the center is on the line\[y = x-7\]
Therefore the center is the point where they intersect:
x-7 = (3/4)x - 7
x = 0, y =-7
Finally, the radius is the distance from (0,-7) to (4,-4)
\[r^{2} = (4-0)^{2} +(-4-(-7))^{2} = 4^{2}+3^{2} = 25\]
Equation of the circle:
\[x^{2}+(y+7)^{2} =25\]

Answer 6

Excellent Solution :D