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Show that the normal at any point \( \theta \) to the curve \( x=a\cos\theta+a\theta\: \sin\theta\) and \( y=a\sin\theta-a\theta \cos\theta\) is at a constant distance from the origin.
cbse
class12
modelpaper
2012
sec-c
q24
math
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asked
Feb 3, 2013
by
thanvigandhi_1
edited
Jul 15, 2013
by
sreemathi.v
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Nov 28, 2012
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Jan 22, 2013
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A curve passing through the point (1,1) has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of p from the x-axis. Determine the equation of the curve.
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Find the equations of the tangent and normal to the curve \( 16x^2+9y^2 = 144\) at \( (x_1, y_1)\) where \( x_1=2\: and \: y_1 > 0.\) Also, find the points of intersection where both tangent and normal cut the \( x\) - axis.
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Jan 9, 2013
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Jan 23, 2013
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A point on the hypotenuse of a right-angled triangle is at distances a and b from the sides. Show that length of the hypotenuse is at least \( (a^{\large\frac{2}{3}}+b^{\large\frac{2}{3}})^{\large\frac{3}{2}} \)
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Jan 26, 2013
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Jan 30, 2013
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