class 11

Math

Co-ordinate Geometry

Hyperbola

The circle $x_{2}+y_{2}−8x=0$ and hyperbola $9x_{2} −4y_{2} =1$ I intersect at the points A and B. Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

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The number of normal (s) of a rectangular hyperbola which can touch its conjugate is equal to

If $PQ$ is a double ordinate of the hyperbola $a_{2}x_{2} −b_{2}y_{2} =1$ such that $OPQ$ is an equilateral triangle, $O$ being the center of the hyperbola, then find the range of the eccentricity $e$ of the hyperbola.

Referred to the principal axes as the axes of coordinates find the equation of the hyperbola whose foci are at $(0,±10 )$ and which passes through the point $(2,3)˙$

The ellipse $25x_{2} +16y_{2} =1$ and the hyperbola $25x_{2} −16y_{2} =1$ have in common

Find the eccentricity of the hyperbola whose latusrectum is half of its transverse axis.

If $P(a,b)$, the point of intersection of the ellipse $a_{2}x_{2} +a_{2}(1−e_{2})y_{2} =1$ and the hyperbola $a_{2}x_{2} −a_{2}(E_{2}−1)y_{2} =41 $ is equidistant from the foci of the two curves (all lying in the right of y-axis), then

Find the area of the triangle formed by any tangent to the hyperbola $a_{2}x_{2} −b_{2}y_{2} =1$ with its asymptotes.

Find the equation of the hyperbola whose foci are $(6,4)and(−4,4)$ and eccentricity is 2.