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Prove that the curves y^2=4x and x^2+y^2...

Prove that the curves `y^2=4x` and `x^2+y^2-6x+1=0` touch each other at the points `(1,\ 2)` .

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To prove that the curves \( y^2 = 4x \) and \( x^2 + y^2 - 6x + 1 = 0 \) touch each other at the point \( (1, 2) \), we will follow these steps: ### Step 1: Differentiate the first curve The first curve is given by: \[ y^2 = 4x \] Differentiating both sides with respect to \( x \): ...
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RD SHARMA ENGLISH-TANGENTS AND NORMALS-All Questions
  1. Find the points on the curve 9y^2=x^3 where normal to the curve makes ...

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  2. Prove that the curves x y=4 and x^2+y^2=8 touch each other.

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  3. Prove that the curves y^2=4x and x^2+y^2-6x+1=0 touch each other at th...

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  4. Show that the angle between the tangent at any point P and the line jo...

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  5. Find the slopes of the tangent and the normal to the curve x^2+3 y2=5 ...

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  6. Show that the tangents to the curve y=x^3-3 at the points where x=2 a...

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  7. Prove that the tangents to the curve y=x^2-5+6 at the points (2,0)a n ...

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  8. The slope of the curve 2y^2=a x^2+ba t(1,-1) is -1 Find a , b

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  9. Find the points on the curve y=x^3-2x^2-x at which the tangent lines a...

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  10. At what points on the curve x^2+y^2-2x-4y+1=0, the tangents are parall...

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  11. Find the required point be P(x1, y1)dot The tangent to the curve sqrt(...

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  12. Show that the curves 2x=y^2a n d2x y=k cut at right angles, if k^2=8.

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  13. Show that the curves x y=a^2a n dx^2+y^2=2a^2 touch each other

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  14. Find the slopes of the tangent and the normal to the curve x^2+3y+y...

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  15. Show that the tangents to the curve y=2x^3-3 at the points where x=...

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  16. Prove that the tangents to the curve y=x^2-5x+6 at the points (2, 0...

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  17. The slope of the curve 2y^2=a x^2+b at (1,\ -1) is -1 . Find a ,\ b .

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  18. Find the slope of the normal to the curve x=1-asintheta , y=b\ cos^...

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  19. Find the slope of the normal to the curve x=a\ cos^3theta , y=a\ sin...

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  20. Find the points on the curve y=x^3-2x^2-x at which the tangent l...

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