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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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We have `y^2 =4x` and `x^2+ y^2 −6x+1=0`
Since both curves touch each other at `(1,2)` i,e, curves are passing
through `(1,2)`
`\therefore 2y. dy/dx=4` ...
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RD SHARMA-TANGENTS AND NORMALS-Solved Examples And Exercises
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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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  11. If the tangent to a curve at a point (x ,\ y) is equally inclined t...

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  12. If the tangent line at a point (x ,\ y) on the curve y=f(x) is para...

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  13. Find the slope of the normal at the point ' t ' on the curve x=1/t ...

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  14. Write the coordinates of the point on the curve y^2=x where the tan...

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  16. Write the equation of the normal to the curve y=x+sinxcosx at x=pi/...

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  17. Find the coordinates of the point on the curve y^2=3-4x where tange...

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  18. Write the equation of the tangent to the curve y=x^2-x+2 at the poin...

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  19. Write the angle between the curves y^2=4x and x^2=2y-3 at the point...

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