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If two curves ax^2 +by^2=1 and a'x^2+b'y...

If two curves `ax^2 +by^2=1` and `a'x^2+b'y^2=1` intersect orthogonally,then show that `1/a-1/b=1/[a']-1/[b']`

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NAGEEN PRAKASHAN-APPLICATIONS OF DERIVATIVES-Exercise 6d
  1. Find the equation of tangent of the curve y^(2) = 4x+5 which is paral...

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  2. Find the equation of tangent of the curve 9x^(2)+16y^(2) = 144 at thos...

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  3. Find the co-ordinates of that point on the curve x^(3)+y^(3)= a^(3) a...

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  4. Find the co-ordinates of that point on the curvey^(2)=x^(2)(1-x) at wh...

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  5. Find the co-ordinates of that point on the curve x^(2)/a^(2)+y^(2)/b^(...

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  6. Prove that the equation of tangent of the ellipse x^(2)/a^(2)+y^(2)/b^...

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  7. Find the value of n in N such that the curve (x/a)^n+(y/b)^n=2 touche...

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  8. Show that the line d/a+y/b=1 touches the curve y=b e^(-x/a) at the poi...

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  9. Find the point on the curve y^(2) = x at which the tangent drawn makes...

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  10. Find the coordinates of the points on the curve y=x^2+3x+4, the tangen...

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  11. The tangent drawn at any point of the curve sqrtx+sqrty = sqrta meets...

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  12. If p and q are the intercept on the axis cut by the tangent of sqrt((x...

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  13. Find the angle of intersection of the curves x y=a^2a n dx^2+y^2=2a^2

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  14. Prove that the curvesx^(2)-y^(2)=16 and xy = 15 intersect each other a...

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  15. If two curves ax^2 +by^2=1 and a'x^2+b'y^2=1 intersect orthogonally,th...

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  16. Prove that the curves "x"="y"^2 and "x y"="k" intersect at right an...

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  17. Find the equation of the tangent and the normal at the point 't, on th...

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  18. Prove that points of the curve y^2=4a{x+asin(x/a)} at which tangents a...

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  19. Prove that the tangents drawn on the parabola y^(2)=4axat points x = a...

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  20. Prove that the curve y^2=4x and x^2 +y^2 - 6x +1=0 touches each other ...

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