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Find the equation of the line through the point ( 3, 4 ) which cuts from the first quadrant a triangle of minimum area.
cbse
class12
modelpaper
2012
sec-c
q24
math
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asked
Jan 7, 2013
by
thanvigandhi_1
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Related questions
Find the equation of the line through the point P(3, 4) which cuts from the first quadrant a triangle of the minimum area. Also find the area of the triangle.
cbse
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2012
sec-c
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A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the minimum length of hypotenuse is \( \bigg[ a^{\large\frac{2}{3}} + b^{\large\frac{2}{3}} \bigg]^{\large\frac{3}{2}} \).
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Find the equation of the plane passing through the intersection of planes \( 4x-y+z=10\: and \: x+y-z=4\) and parallel to the line with direction ratios < 2, 1, 1>. Find also the perpendicular distance of (1, 1, 1) from the plane.
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Find the equation of the plane passing through the line of intersection of the planes $ 2x+y-z=3 \: and \: 5x-3y+4z+9=0$ and parallel to the line \(\large \frac{x-1}{2}=\frac{y-3}{4}=\frac{z-5}{5}. \)
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A wire of length 36 cm is cut into two pieces. One of the pieces is turned in the form of a square and the other in the form of an equilateral triangle. Find the length of each piece so that the sum of the areas of the two be minimum.
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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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Show that the cylinder of given volume open at the top has minimum total surface area if its height is equal to radius of the base.
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2012
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