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Show that the line y = mx + c touches th...

Show that the line y = mx + c touches the ellips
`x^2/a^2 + y^2/b^2 = 1 if c^2 = a^2m^2 + b^2`.

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Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = (a)/(m) .

The line y=x+2 is a tangent to the ellipse x^2/2+y^2/1=1

Prove that the line xcosalpha+ysinalpha=p touches the ellipse (x^2/a^2+y^2/b^2)=1 If p^2=a^2coas^2alpha+b^2sin^2alpha .

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If the straight line x cos alpha + y sin alpha = p touches the curve (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 , then prove that a^(2) cos^(2) alpha + b^(2) sin^(2) alpha = p^(2) .

MBD PUBLICATION-APPLICATION OF DERIVATIVES-QUESTION BANK
  1. Find the point on the curve x^2 + y^2 - 4xy + 2 = 0 where the normal...

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  2. Show that the line y = mx + c touchees y = 4ax if c = a/m.

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  3. Show that the line y = mx + c touches the ellips x^2/a^2 + y^2/b^2 =...

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  4. Show that the sum of the intercepts on the coordinate axes of any tang...

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  5. Show that the curves y = 2^(x) and y = 5^(x) intersect at an angle tan...

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  6. Show that the curves ax^2 + by^2 = 1 and a' x^2 + b' y^2 = 1. Interse...

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  7. Find the equasion of the tangents drawn from the point (1,2) to the cu...

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  8. Show that the equation of the normal to x^(2/3) + y^(2/3) = a^(2/3)is ...

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  9. Show that the length of the portion of the tangent to x^(2/3) + y^(2/3...

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  10. Find the tangent to the curve y = cos (x + y), 0 lt x lt 2 pi which...

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  11. If tangents are drawn from the origin to the curve y = sin x then sho...

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  12. Find the equation of the normal to the curve given by x = 3 cos thet...

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  13. If x cos alpha + y sin alpha = p is a tangent to the curve (x/a)^(n/...

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  14. Show that the tangent to the curve x = a (t - sin t), y = at (1 + cos ...

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  15. Find the intervals where the following functions are (a) increasing an...

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  16. Find the intervals where the following functions are (a) increasing an...

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  17. Find the intervals where the following functions are (a) increasing an...

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  18. Find the intervals where the following functions are (a) increasing an...

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  19. Find the intervals where the following functions are (a) increasing an...

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  20. Find the intervals where the following functions are (a) increasing an...

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