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Find the reflection of the point (2, 1) with respect to the line x=y in the xy-plane.

Find the area of the circle in the xy-plane which has its centre at the point (1,2) and which has the line x=y as a tangent.

Find the incentre of the triangle in the xy-plane whose sides are given by the lines x=0 , y=0 and

Let A and B be fixed points in a plane such that, the length of the line segment AB is d. Let the point P describe an ellipse by moving on the plane such that the sum of the lengths of the line segments PA and PB is a constant l. Express the length of the semi-major axis, a and the length of the semi-minor axis, b, of the ellipse in terms of d and l.

Let A = be a non-zero symmetric matrix with real entries. LetÂ S = { }. Which of the following conditions imply that S is unbounded?

det(A) > 0.

det(A) = 0

det(A) < 0.

Let Â define an invertible linear transformation on . Let T be a triangle with one of its vertices at the origin and of area a. What is the area of the triangle which is the image of T under this transformation’?

Find the area of the ellipse whose equation in the xy plane is given by .

Let a, b and c be positive real numbers. Find the equation of the sphere which passes through the origin and through the points where the plane meets the coordinate axes.

Consider the sphere .Â Let be a point in the interior of this sphere. Write down the equation of the plane whose intersection with the sphere is a circle whose center is the point (a, b, c) .

Find the area of the polygon whose vertices are represented by the eighth roots of unity.

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