class 11

Math

Co-ordinate Geometry

Hyperbola

Tangents are drawn to the hyperbola $4x_{2}−y_{2}=36$ at the points P and Q. If these tangents intersect at the point T(0,3) then the area (in sq units) of $△PTQ$ is

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Two rods are rotating about two fixed points in opposite directions. If they start from their position of coincidence and one rotates at the rate double that of the other, then find the locus of point of the intersection of the two rods.

If $e_{1}ande_{2}$ are respectively the eccentricities of the ellipse $18x_{2} +4y_{2} =1$ and the hyperbola $9x_{2} −4y_{2} =1,$ then the relation between $e_{1}ande_{2}$ is a.$2e_{1}+e_{2}=3$ b. $e_{1}+2e_{2}=3$ c. $2e_{1}+e_{2}=3$ d. $e_{1}+3e_{2}=2$

The foci of the hyperbola $2x_{2}−3y_{2}=5$ are a.$(±56 ,0)$ b. $(±5/6,0)$ c. $(±5 /6,0)$ d. none of these

Find the eccentricity, coordinates of the foci, equations of directrices and length of the latus rectum of the hyperbola $16x_{2}−9y_{2}=144$

$PQ$ and $RS$ are two perpendicular chords of the rectangular hyperbola $xy=c_{2}˙$ If $C$ is the center of the rectangular hyperbola, then find the value of product of the slopes of $CP,CQ,CR,$ and $CS˙$

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

$OA$ and $OB$ are fixed straight lines, $P$ is any point and $PM$ and $PN$ are the perpendiculars from $P$ on $OAandOB,$ respectively. Find the locus of $P$ if the quadrilateral $OMPN$ is of constant area.

If the vertices of the hyperbola be at $(−2,0)$ and $(2,0)$ and one of the foci be at $(−3,0)$ then which one of the following points does not lie on the hyperbola? (a) $(−6,210 )$ (b) $(26 ,5)$ (c) $(4,15 )$ (d) $(6,52 )$