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Show that the curves (x^2)/(a^2+lambda1)...

Show that the curves `(x^2)/(a^2+lambda_1)+(y^2)/(b^2+lambda_1)=1` and `(x^2)/(a^2+lambda_2)+(y^2)/(b^2+lambda_2)=1` intersect at right angles.

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To show that the curves \[ \frac{x^2}{a^2 + \lambda_1} + \frac{y^2}{b^2 + \lambda_1} = 1 \] and ...
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RD SHARMA-TANGENTS AND NORMALS-Solved Examples And Exercises
  1. Show that the curves (x^2)/(a^2+lambda1)+(y^2)/(b^2+lambda1)=1 and (x^...

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  2. Find the condition for the following set of curves to intersect ort...

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  3. Show that the following set of curves intersect orthogonally: (i) y=x...

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  4. Find the angle of intersection of the following curves : (i)y^2=xa n...

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  5. Show that the curves 4x=y^2 and 4x y=k cut at right angles, if k^2=...

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  6. Find the equation of the tangent to the curve sqrt(x)+sqrt(y)=a , at t...

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  7. Find a point on the curve y=x^3-3x where the tangent is parallel to th...

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  8. Find the points on the curve x y+4=0 at which the tangents are incline...

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  9. Find the equation of normal line to the curve y=x^3+2x+6 which is para...

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  10. Find the slopes of the tangent and the normal to the following curves ...

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  11. If the tangent to the curve y=x^3+a x+b at (1,-6) is parallel to the l...

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  12. Find the equation of the tangent to the curve x=sin3t ,y=cos2t at t=pi...

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  13. Prove that (x/a)^n+(y/b)^n=2 touches the straight line x/a+y/b=2 fo...

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  14. At what point on the circle x^2+y^2-2x-4y+1=0, the tangent is paralle...

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  15. Find the point on the curve y=x^2 where the slope of the tangent is eq...

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  16. At what point will be tangents to the curve y=2x^3-15 x^2+36 x-21 by p...

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  17. If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^...

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  18. Find the point on the curve y=3x^2+4 at which the tangent is perpendic...

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  19. Find the equation of the normal to y=2x^3-x^2+3 at (1,4).

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  20. Find the point on the curve y=3x^2-9x+8 at which the tangents are equa...

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