Answer:
<h2>
A(-2, 2) and B(6, 10)</h2>
Step-by-step explanation:
Given the equation of a line y = x + 4 and equation of a circle as
( x − 3 )² + ( y − 5 )² = 34, if the line and the circle intersect at points A and B, to get this points, we will substitute the equation of the line into that of the circle as shown;
We will have to expand the equation of the circle first before making the substitute.
( x − 3 )² + ( y − 5 )² = 34
x²-6x+9+y²-10y+25 = 34
x²+y²-6x+-10y+34-34 = 0
x²+y²-6x+-10y = 0
Substituting y = x+ 4 into the resulting expression;
x²+(x+4)²-6x+-10y = 0
x²+x²+8x+16-6x+-10(x+4) = 0
x²+x²+8x+16-6x+-10x-40 = 0
2x²-8x-24 = 0
x²-4x-12 = 0
(x²-6x)+(2x-12) = 0
x(x-6)+2(x-6) = 0
x+2 = 0 and x-6 = 0
x = -2 and 6
when x = -2;
y = -2+4
y = 2
when x = 6
y = 6+4
y = 10
The coordinates of the point of intersection are A(-2, 2) and B(6, 10).
