Question

If the tangent to the curve 3xy^2-2x^2y=1
at (1,1) intersect the curve again at (alpha,beta) then find (alpha,beta)

Answer 1

\[\Huge 3xy^2-2x^2y=1\]

Answer 2

find the equation of the line and find the points of intersection.

Answer 3

\[\LARGE 3y^2+6xy \frac{dy}{dx}-(4xy+2x^2 \frac{dy}{dx})=0\]
\[\LARGE \frac{dy}{dx}=\frac{4xy-3y^2}{6xy-2x^2}\]

Answer 4

plug in 1,1

Answer 5

4-3/6-2
1/4

Answer 6

Then use y-1 = m(x-1) to find the line equation

Answer 7

y-1=1/4(x-1)

Answer 8

4y-4=x-1
4y-x-3=0

Answer 9

Yeah, solve the equations.