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As we know the equation of ellipse in polar form is $x=a\cos \theta$ and $y=b\sin \theta$.

What is the equation of the parabola $y^2=4ax$ in polar form? Please help me.

Ng Chung Tak
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cseju19
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    Hint: $y=r\sin\theta, x=r\cos\theta$ – J. W. Tanner Jul 26 '19 at 15:26
  • what is r in case of parabola? – cseju19 Jul 26 '19 at 15:28
  • The polar form of an equation involves $r$ and $\theta$. You have given a common parametric form of an ellipse, but it it not the polar form. So ... What are you really wanting? – Blue Jul 26 '19 at 15:28
  • The parametric form of parametric form of parabola for y2=4ax is x=at^2, y=2at. what is t here? – cseju19 Jul 26 '19 at 15:30
  • I want in parametric form. For a point on the axis of symmetry, I want to find out the nearest point on the perimeter of parabola. Thats I want equation in the form of angle. please help. – cseju19 Jul 26 '19 at 15:33
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    In $x=at^2$, $y=2at$, the $t$ value is simply a parameter that guides $x$ and $y$, but it is not the angle made by a given point. For what you're trying to do, it doesn't matter. You don't need an equation that uses an angle, you just need $x$ and $y$ to be related by a third value (the parameter $t$). – Blue Jul 26 '19 at 15:33
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    For a point, say, $(p,0)$ on the axis of symmetry, write an expression for the distance to $(x,y)=(at^2,2at)$. Then find $t$-values that minimize your expression. (Actually, it's more-convenient to minimize the square of that expression. The results are the same.) It doesn't matter what $t$ represents geometrically. When you find the minimizing $t$-values, you simply substitute them back into $(x,y)=(at^2,2at)$ to get the corresponding points. – Blue Jul 26 '19 at 15:38

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