Calendar: 1859-1860 Page 445

446 GENERAL LITERATURE AND SCIENCE parabola whose latus rectum is one-fourth of that of the given one If triangle formed by pair of tangents to an ellipse and the chord of contact be of constant area find the locus of its vertex If parabola moves so as always to touch two straight lines at right angles to one another its vertex describes the curve xiyi xi- -yl a2 figure made up of rectangle and an isosceles triangle is inscribed in semicircle determine its dimensions so that its area may be maximum MATHEMATICS -JUNIOR SCHOLARSHIP -Silgtbra Find the value of I'x'6- y2 Zy3 when χ Find the product of x2 -f y2 χ xy by χ χ and χ χ Divide 8a4- 22a3£ 43a2£2 38a£a 2444 by 2a2 3ab 4b2 x3 -f x1 ab -ac- -bc x- abc by χ What value of χ will make the following true result x2 3χ χ Reduce to single fractions- a2 C2 2' 2c ac2 β ז ac2 -c2 -2ac -c2 2a Extract the square roots of 25 30aa 49a2 x2 24 a3 16a4