# Geometry

Find the points of intersection of the line X+Y=5, and the circle x^2+y^2=25 by solving the system of equations.

1. 👍
2. 👎
3. 👁
1. well, y = 5-x, so

x^2 + (5-x)^2 = 25

now just expand and solve the quadratic.

1. 👍
2. 👎
2. x+5/30=4x-10/75

2*3*5*5*(x+5)/2*3*5=2*3*5*5(4x-10)/3*5*5

5*(x+5)=2*(4x-10)
5x+25=8x-20
25+20=3x
3x=45
x=15

1. 👍
2. 👎
3. x=0, y=0
x=5,y=25
no other solutions

1. 👍
2. 👎
4. The x=15 is ok

Not sure what the last set of values is for, but if they are for the 1st problem, no good.

x^2 + (5-x)^2 = 25
x^2 + x^2-10x+25 = 25
2x^2-10x = 0
2x(x-5) = 0

x = 0 or x=5

So, the points of intersection are (0,5) and (5,0)

1. 👍
2. 👎

## Similar Questions

1. ### math

Let L1 be the line passing through the points Q1=(4, −1, −2) and Q2=(1, 0, −1) and let L2 be the line passing through the point P1=(−6, 21, −8) with direction vector →d=[−3, 9, −3]T. Determine whether L1 and L2

2. ### Algebra

Let L1 be the line passing through the points Q1=(−2, −3, −4) and Q2=(−5, −2, −3) and let L2 be the line passing through the point P1=(−27, 31, −25) with direction vector →d=[−6, 9, −6]T. Determine whether L1

3. ### hch

Let L1 be the line passing through the points Q1=(2, −2, 5) and Q2=(−4, −6, 3) and let L2 be the line passing through the point P1=(7, 4, 0) with direction vector →d=[−1, −2, 3]T. Determine whether L1 and L2 intersect.

4. ### calc

standard equation of circle concentric with X^2+Y^2-2X-8Y+1=0 and tangent to line 2X-Y=3 Complete the squares to find the center of the circle. X^2+Y^2-2X-8Y+1=0 (x-1)^2+(y-4)^2 - 16 =0 The center is (1,4) and the radius for the

1. ### Calculus

A circle C has center at the origin and radius 9. Another circle K has a diameter with one end at the origin and the other end at the point (0,17). The circles C and K intersect in two points. Let P be the point of intersection of

2. ### geometry

n the xy -plane, the graph of y = x^2 and the circle with center (0,1) and radius 3 have how many points of intersection?

3. ### can you answer this very quick

On a graph, the solution to a system of linear equations will be represented by ______. A. the x-intercept of each line B. the y-intercept of each line C. all the points on either line D. the intersection of the lines

4. ### maths

The points of intersection of two equal circles which cut orthogonally are (2,3) and (5,4). Then radius of each circle is?

1. ### Calculus

The circle defined by the equation x^2 + y^2 = 18 has two points where the slope of its tangent line is m=1. Find those points.

2. ### Math

The line has equation y=2x+c and a curve has equation y=8-2x-x^2. 1) for the case where the line is a tangent to the curve, find the value of the constant c. 2) For the case where c = 11, find the x-coordinates of the points of

3. ### calculus

a) If x3 + y3 - xy2 = 5, find dy/dx. (b) Using your answer to part (a), make a table of approximate y-values of points on the curve near x = 1, y = 2. Include x = 0.96, 0.98, 1, 1.02, 1.04. (c) Find the y-value for x = 0.96 by

4. ### maths

P(6,3), Q(3,7), and R(4,2) are three points in a plane. A is the midpoint of QR and B is the foot of the perpendicular from Q to PR. Find;- (A) the cordinates of A; (B) the equations of the lines PA and QB; (C) the point of