4x² + 2√√3xy + 2y² = 1 ugh what angle should the axes be rotated so that the term xy e the transformed equation. etermine x so that the line passing through the point (3, 4) and angle of135° with the positive direction of the y. ayis
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- when the axes are rotated through an angle x/4,find the transformed equation of 3x2+10xy+3y2=9When the axes are rotated through an angle 4π, find the transformed equation of3x2+ 10xy + 3y2= 9.Find an equation of the line L that passes through the point (−4, 7) and satisfies the condition. L is perpendicular to the line 7x + 6y = 7
- (a) If the abscissa and ordinates of two points P and Q are the roots ofthe equations x\power{2}+2ax-b\power{2}=0 and x\power{2}+2px-q\power{2}=0 respectively,then find the equation of the circle with PQ as diameter. (b)Find the equation of the circle which passes through (1, 0) and (0, 1) and has its radius as small as possible.A, B, and C are collinear points: B is between A and C. If AB = 36, BC = 5x - 9, and AC = 54, find x. I am doing the work myself and checking it against the experts.(a) A circle passes through the origin and has its center on y=x.if it cuts x2 +y2 -4x-6y+10=0 orthogonally,then find the equation of the circle.(b) The equation of three circles are given x2 +y2 -1,x2 -y2 -8x+15=0,x2 +y2 +10x+24=0 Determine the coordinates of the point P such that the tangents drawn from it to the circles are equal in length.
- Find an equation for the plane through P0(-3, 0, 7) perpendicular to n = 5i + 2j - k.The coordinates of B' after a reflection across the line y=-2 areFind a general form of an equation of the line through the point A that satisfies the given condition. A(9, −3); perpendicular to the line 2x − 2y = 3