"Find the y-intercept of a given parametric curve...." was answered by our experts

High School
Statistics and Probability
High school statistics
Y-Intercept

April Bush

Answered question

2022-06-15

Find the

y

-intercept of a given parametric curve.

x = t (t^{2} - 3)

y = 3 (t^{2} - 3)

Answer & Explanation

Hadley Cunningham

Beginner2022-06-16Added 20 answers

The y intercepts of a curve are the points at which the curve intersects the

y

-axis (i.e. the curve may be a line and may be not, so the

y

-intercept is not only the

b

in the equation

y = m x + b

)
Also when the curve intersects the y-axis, it means that the

x = 0

t (t^{2} - 3) = 0 ⟹ t = 0

t = \pm \sqrt{3}

Karina Trujillo

Beginner2022-06-17Added 4 answers

We have

x = t (t^{2} - 3)

and

y = 3 (t^{2} - 3)

\frac{x}{y} = \frac{t}{3} \Rightarrow t = \frac{3 x}{y}

So substituting this value of t in any of the parametric expression in

t

for

x

y

we get an equation in

x

and

y

. Further we can put

x = 0

to get the y intercept.

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