SOLUTION: What point is the intersection of the graphs of x^2 + y^2 = 25 and y = x + 7?

 

Hi,

What point is the intersection of the graphs: 

x^2 + y^2 = 25   circle C(0,0) and radius = 5  (See below)

y = x + 7        Line:  Pt(0,7) and Pt(-7,0) on the Line

algebraically:  substituting (x+7) for y

x^2 + (x+7)^2= 25

2x^2 +14y + 24 =(2x+6)(x+4)  |tossing out x = -3 as Extraneous

x = -4 then y = 3   (y = -4+7)

Graphs: parbola and Line intersect at:(-4,3)





Standard Form of an Equation of a Circle is  

where Pt(h,k) is the center and r is the radius



 Standard Form of an Equation of an Ellipse is 

where Pt(h,k) is the center and a and b  are the respective vertices distances from center.



Standard Form of an Equation of an Hyperbola opening right and  left is:

   where Pt(h,k) is a center  with vertices 'a' units right and left of center.

Standard Form of an Equation of an Hyperbola opening up and down is:

   where Pt(h,k) is a center  with vertices 'b' units up and down from center.



The vertex form of a parabola opening up or down,  where(h,k) is the vertex.

The standard form is , where  the focus is (h,k + p)



The vertex form of a parabola opening right or left,  where(h,k) is the vertex.

The standard form is , where  the focus is (h +p,k )