Question

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.

Answer 1

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 \(y\).

Answer 2

@sithsandgiggles okay I will do that. Thank you