Answer to Question #307585 in Analytic Geometry for Cee

Question

Find the parametric equations of the line that is going through the point (6,9,5) and is parallel to the plane 8x+6y+8z=9 and is perpendicular to the line

⟨x,y,z⟩=⟨7,9,4⟩+⟨5,4,6⟩t

x= Blank 1. Calculate the answer by read surrounding text.

+( Blank 2. Calculate the answer by read surrounding text.

)t, y= Blank 3. Calculate the answer by read surrounding text.

+( Blank 4. Calculate the answer by read surrounding text.

)t, z= Blank 5. Calculate the answer by read surrounding text.

+(2) t

Answer 1

Calculation of intersection points:

y=3x+7equation (1)

y=x²+2x+1

equation (2)

y=3x+7equation (1)y=x2+2x+1equation (2)

equating equations (1) and (2):

x²+2x+2x+1=3x+7x2+2x+1−3x−7=0x2−x−6=0(x−3)(x+2)=0

The solution of the previous equation is:

x1=3x²=−2x1=3x²=−2

So:

y1=3(3)+7 =

16y²=3(−2)+7=1y1=3(3)+7=16y²=3(+1

.Therefore the intersection points

are:

P1(−2,1)P2

(3,1)

P1(−2,1)P2(3,16)