Find the points on the ellipse a2x2+b2y2=1
such that the tangent at each point makes equal angles with the axes.
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An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?
If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices ofthe quadrilateral, prove that it is a rectangle
If a vertex, the circumcenter, and the centroid of a triangle are (0, 0), (3,4), and (6, 8), respectively, then the triangle must be (a) a right-angled triangle (b) an equilateral triangle (c) an isosceles triangle (d) a right-angled isosceles triangle
into its equivalent Cartesian equation.
At what point should the origin be shifted if the coordinates of a point (4,5)
The line joining the points (x,2x)and(3,5)
makes an obtuse angle with the positive direction of the x-axis. Then find the values of x˙
Find the centre and radius of the circlesx2+y2−8x+10y−12=0
internally in the ratio λ1:λ2
externally in the ratio λ1;λ2,
then prove that OA
is the harmonic mean of OP