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Prove that the tangents to the curve y=x...

Prove that the tangents to the curve `y=x^2 - 5x + 6` at the points (2,0) and (3,0) are at right-angles.

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MODERN PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE
  1. Find the equation of all lines having slope 2 which are tangent to the...

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  2. Find the point of intersection of the tangetn lines to the curve y = 2...

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  3. Prove that the tangents to the curve y=x^2 - 5x + 6 at the points (2,0...

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  4. Find the angle of intersection of the curves: y^2=4x and x^2=4y

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  5. Find the angle of intersection of the curves: x^2+y^2-4x-1=0 and x^2+y...

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  6. Show that the following curves cut each other orthogonally: y = x^3 an...

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  7. Show that the following curves cut each other orthogonally: x^2 + 4y^2...

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  8. If the curves: alphax^2 + betay^2 =1 and alpha'x^2 + beta'y^2=1 inters...

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  9. Prove that the curves 4x = y^2 and 4xy = k cut at right angles if k^2...

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  10. Show that the curves 2x = y^2 and 2xy = k cut at right angles if k^2 =...

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  11. Prove that the curves y^(2)=4axandxy=c^(2) cut at right angles if c^(4...

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  12. Show that the normal at any point theta to the curve x = a cos theta +...

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  13. Find the equations of the tangent and normal to the curve 16x^2 + 9y^2...

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  14. Find a point on the curve y=x^(3), where the tangent to the curve is p...

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  15. Find a point on the parabola y =(x-3)^2, where the tangent is parallel...

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  16. Show that the area of the triangle formed by the tangent and the norma...

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  17. Find the equations of the normal at a point on the curve x^2=4y, which...

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  18. Find the equations of the tangents to the curve 3x^2 - y^2 = 8, which ...

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  19. Determine the values of 'x' for which the function f(x) = x^2 + 2x - 3...

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  20. Determine the intervals in which the function f(x) = (x-1)(x+1)^2 is i...

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