The curve C has equation 2x^2 + y^2 = 18. Determine the coordinates of the four points on C at which the normal passes through the point (1,0). Non-calculator question.

Question

anonymous · Answer

Find the derivative $\dfrac{dy}{dx}$ (or $\dfrac{dx}{dy}$). This gives the slope of the line tangent to $C$ at point $(x,y)$.

The line normal to the curve at the same points will have a negative reciprocal slope. (i.e. if you find $\dfrac{dy}{dx}=x$, for instance, then the slope of the normal would be $-\dfrac{1}{x}$.)

Use the point-slope formula to find the equation of the normal line through (1,0) and find the respective values of $x$ and $y$.

anonymous · Answer

@sithsandgiggles okay I will do that. Thank you