Answer:
(3,-4) and (-3,4)
Step-by-step explanation:
[tex]x^2+y^2=25[/tex]
[tex]4x+3y=0[/tex]
The first equation is a circle with radius of 5 units
The second equation is a line which has slope [tex]\frac{4}{3}[/tex]
So, for 4 unit change in y there will be 3 unit chang in x.
The circle has its center at the origin and the line passes through the orgin.
The line will intersect the circle at two points giving us two solutions
From the second equation we get
[tex]y=-\frac{4}{3}x[/tex]
Applying in the second equation
[tex]x^2+\left(-\frac{4}{3}x\right)^2=25\\\Rightarrow x^2+\frac{16}{9}x^2=25\\\Rightarrow \frac{9x^2+16x^2}{9}=25\\\Rightarrow 25x^2=225\\\Rightarrow x^2=\frac{225}{25}\\\Rightarrow x^2=9\\\Rightarrow x=\pm 3[/tex]
When x = 3
[tex]y=-\frac{4}{3}x\\\Rightarrow y=-\frac{4}{3}\times 3\\\Rightarrow y=-4[/tex]
When x = -3
[tex]y=-\frac{4}{3}x\\\Rightarrow y=-\frac{4}{3}\times -3\\\Rightarrow y=4[/tex]
So, the points where the line and circle intersect are (3,-4) and (-3,4)
