PARAMETER AND PARAMETRIC EQUATION

# PARAMETER AND PARAMETRIC EQUATION

C
Asked by 1 month ago
10 million points

Find the coordinates of the points where the line $4x-5y+6a=0$ cuts the curve given parametrically by $(at^2, 2at)$.

PARAMETER AND
chegendungu

C
Answered by 1 month ago
10 million points

If the line $4x-5y+6a=0$ meets the curve at the point $(at^2, 2at)$, then its coordinates must satisfy the equation of the line. Therefore

$4at^2-10at+6a=0$

$\therefore 2t^2-5t+3=0$

$\therefore (2t-3)(t-1)=0$

$\therefore t=\frac{3}{2}$ or $1$

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