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show that the tangent to y^2= 4ax at (a,-2a) touches the parabola x^2= 4ay.

show that the tangent to y^2= 4ax at (a,-2a) touches the parabola x^2= 4ay. 

Grade:11

1 Answers

Vikas TU
14149 Points
4 years ago
Differntiate y^2= 4ax,
2y.dy/dx = 4a
dy/dx = 2a/y
dy/dx = 2a/-2a = -1
 
Thus for x^2 = 4ay the slope should also come to -1 as they both have a common tangent.
Now doing,
2x = 4ady/dx2
dy/dx2 = x/2a = > a/2a = 0.5
hence dy/dx is not equal to dy/dx2.
Hence the tangent is not common.
Moreover, that point either doesn't lies on x^2=4ay.
Sp plz xcheck your question. 

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