Question
Prove: The line tangent to the parabola $x^{2}=4 p y$ at the point $\left(x_{0}, y_{0}\right)$ is $x_{0} x=2 p\left(y+y_{0}\right)$
Step 1
Step 1: Given the parabola $x^{2}=4 p y$ and a point on the parabola $\left(x_{0}, y_{0}\right)$, we want to find the equation of the tangent line at this point. Show more…
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(a) Show that the equation of the tangent line to the parabola $y^{2}=4 p x$ at the point $\left(x_{0}, y_{0}\right)$ can be written as $$y_{0} y=2 p\left(x+x_{0}\right)$$ (b) What is the $x$ -intercept of this tangent line? Use this fac to draw the tangent line.
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(a) Show that the equation of the tangent line to the parabola $y^{2}=4 p x$ at the point $\left(x_{0}, y_{0}\right)$ can be written as $$y_{0} y=2 p\left(x+x_{0}\right)$$ (b) What is the $x$ -intercept of this tangent line? Use this fact to draw the tangent line.
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