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Prove that the line x+y=3a touches the c...

Prove that the line `x+y=3a` touches the curve `x^(3)+y^(3)=3axy,` find the coordinnates of the points of contact.

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The correct Answer is:
`((3a)/(2),(3a)/(2))`
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CHHAYA PUBLICATION-TANGENT AND NORMAL -LONG ANSWER TYPE QUESTIONS
  1. Show that the straight line (x)/(a)+(y)/(b)=2 touches the curve ((x)/(...

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  2. Prove that the line x+y=3a touches the curve x^(3)+y^(3)=3axy, find th...

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  3. Find the equation of the tangent to the parabola y^2 = 4x + 5 which is...

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  4. Find the equation of tangnets to the hyperbola (x^(2))/(25)-(y^(2))/(3...

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  5. Find the equation of the tangents to the parabola 3y^(2)=8x, parallel ...

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  6. Find the equation of the tangent to the ellipse 2x^(2)+3y^(2)=30, whic...

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  7. Find the equation of the tangents to the cirlce x^(2)+y^(2)=81 which a...

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  8. Find the equation of the tangent to the parabola y^(2)=8x at the point...

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  9. Find the equations of the tangents ot the ellipse x^(2)+3y^(2)=4 which...

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  10. Find the equation of the tangent, perpendicular to the line x+2y=0, to...

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  11. If the straight line lx+my+n=0 touches the : circle x^(2)+y^(2)=a^(...

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  12. If the straight line lx+my+n=0 touches the : circle x^(2)+y^(2)+2ag...

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  13. If the straight line lx+my+n=0 touches the : parabola y^(2)=4ax, pr...

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  14. Find the condition that the straight line lx+my=n touches the ellipse ...

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  15. If the straight line lx+my+n=0 touches the : hyperbola (x^(2))/(a^(2...

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  16. If the straight line y= x sin alpha+ a sec alpha be a tangent ot the c...

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  17. Find the condition that the straight line x cos theta+ y sin theta =p ...

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  18. Find the condition that the straight line x cos alpha+ y sin alpha=p i...

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  19. hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1.

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  20. If the straight line lx+my=1 touches th curve (ax)^(n)+(by)^(n)=1. The...

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