Find a curve through (-1, 3) orthogonal to every parabola of the form y=1+cx^2 that it intersects.

Question

idealist10 · Answer

@SithsAndGiggles

anonymous · Answer

orthogonal slope =-1/(slope of a line)

idealist10 · Answer

So how do I do this problem?

anonymous · Answer

take the derivative of equation this will give the tangent line equation. 
the slope of orthogonal =-1/tangent slope

idealist10 · Answer

Take the derivative of y=1+cx^2 with respect to x?

anonymous · Answer

y1-y2=m(x1-x2)
(x2,y2)=(-1,3)
y-3=m(x+1)    you need m  which is equal -1/m

anonymous · Answer

yes

idealist10 · Answer

So I got dy/dx=2cx, now what?

anonymous · Answer

This is essentially an initial-value version of your previous orthogonal trajectory problems.

Set up your ODE, then solve for $y$ to find a family of solution curves, and finally plug in $x=-1$ and $y=3$ to determine the particular curve for this problem.

idealist10 · Answer

OMG! It was so easy! I was over-thinking. Thank you for the hint.