Help with Conics (1 Viewer)

[sincred91]

i Dont know how to apprach these questions,
need to find the normals and tangents of the following parabolas at certain points.

please show working

y^2=2(x-3) at point (5,2)

x-cos2theta, y=costheta at point where theta=pi/4

y=(x-2)^2 at point (3,1)

x=cos2t, y=sint at point where t=0

x=t+3, y=t^2-5 at point where t=1

(y-2)^2=4(x-1) at the vertex.

thanks.

 

[Timothy.Siu]

y^2=2(x-3) at point (5,2)

y^2=2x-6
2y(dy/dx)=2
dy/dx=1/y when y=2 dy/dx=2
i think thats right, then u just use point gradient fformula, gradient is 2 for tangent and -1/2 for normal

x-cos2theta, y=costheta at point where theta=pi/4
supposed to be x=cos2theta?
x=2cos^2 theta - 1
sub in y, x=2y^2-1
1=2y(dy/dx)
dy/dx=(1/2y) at pi/4, y=1/root2
dy/dx=root2/2 i hope thats right, same as above point gradient formula, theta=pi/4 x=0
y=(x-2)^2 at point (3,1)
dy/dx=2(x-2)
dy/dx=2 when x=3 same as above
x=cos2t, y=sint at point where t=0
basically same as 2 above

cbb