A tangent having slope of −34
to the ellipse 18x2+32y2=1
intersects the major and minor axes at points AandB,
respectively. If C
is the center of the ellipse, then find area of triangle ABC˙
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If the circumcenter of an acute-angled triangle lies at the origin and the centroid is the middle point of the line joining the points (a2+1,a2+1)
then find the orthocentre.
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.25x2+100y2=1
is the origin and if the coordinates of any two points Q1andQ2
respectively, prove that OQ1O˙Q2cos∠Q1OQ2=x1x2+y1y2˙
Find the equations of the hyperbola satisfying the given conditions :Vertices (±2,0),foci(±3,0)
The equation of curve referred to the new axes, axes retaining their directions, and origin (4,5)
. Find the equation referred to the original axes.
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
Find the equations of the hyperbola satisfying the given conditions :Vertices (0,±3),foci(0,±5)
Two circles of radii 5 cm and 3cm
intersect at two points and the distance between their centres is 4cm˙
Find the length of the common chord.