class 11

Math

Co-ordinate Geometry

Conic Sections

A focus of an ellipse is at the origin. The directrix is the line $x=4$and the eccentricity is 1/2. Then the length of the semimajor axis is

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The vertices of a triangle are $A(x_{1},x_{1},tanθ_{1}),B(x_{2},x_{2},tanθ_{2})$ and $C(x_{3},x_{3},tanθ_{3})$. 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 $(0,0),(3,0),$ and $(0,4)˙$

Find the coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas:(i) $9x_{2} −16y_{2} =1$ (ii) $y_{2}−16x_{2}=1$

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 $(A(5,−1),B(−1,5),$ and $C(6,6)˙$ 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 $x˙$