Calendar: 1890-1891 Page 761

ENGINEERING DEPARTMENT Xcix AHL are that point prove that the sides of the triangle perpendicular respectively to the sides of the triangle CBF point Ρ moves so that the square of its perpendicular on the diagonal of square is equal to the product of the perpendiculars on the two adjacent sides which meet on the other diagonal prove that the locus of Ρ is circle and find the centre and radius of this circle 10 State the meaning of and ρ in the equation χ cos j- sin ρ and shew how an equation Ax By may be converted into that form Find the distance between tho straight lines 5x 12y 15 and 5x -f 12y the unit distance being one inch 11 Find the condition that Ix -f my ρ may be tangent to the circle x2 -f y1 a2 an verify that 2s ac is common tangent to the given circle and to y2 c1 12 point Ρ moves in plane so that the sum of the squares of its distances from three sides of given square is equal to the square of its distance from the remaining side of the square Shew that the locus of Ρ is parabola and trace the part of the curve which lies within the given square &eonutr If two straight lines be parallel to each other and one of them be at right angles to plane the other shall also be at right angles to the same plane ΛΒ and CO are two ηοη-intersectmg straight lines in space CE is drawn parallel to AB Aff BK are perpendiculars to the plane ECO and Η Κ meets CD in shew that LM drawn parallel to AH or BK is common perpendicular to AB and CD