A focus of an ellipse is at the origin. The directrix is the line x=4and the eccentricity is 1/2. Then the length of the semimajor axis is
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The vertices of a triangle are A(x1,x1,tanθ1),B(x2,x2,tanθ2) and C(x3,x3,tanθ3). If the circumcentre coincides with origin then
Find the equations of the hyperbola satisfying the given conditions :Vertices (0,±3),foci(0,±5)
Find the equations of the hyperbola satisfying the given conditions :Vertices (±7,0), e=34
Find the orthocentre of the triangle whose vertices are (0,0),(3,0),
Find the coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas:(i) 9x2−16y2=1 (ii) y2−16x2=1
Find the equations of the hyperbola satisfying the given conditions :Foci (±5,0), the transverse axis is of length 8.
Find the coordinates of the circumcenter of the triangle whose vertices are (A(5,−1),B(−1,5),
Find its radius also.
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˙