Question

The slope of the tangent at $(2,3)$ on the parabola $y^2=\frac{9}{2}x$ is m. Find 4m

Answer 1

Point $(2,3)$

The equation of parabola is $y^2=\frac{9}{2}x2y\frac{dy}{dx}=\frac{9}{2}{\frac{dy}{dx}|}_{(2,3)}=\frac{3}{4}$

The equation of tangent is $(y-3)=\frac{3}{4}(x-2)4y-12=3x-6=03x-4y+6=0$