class 11

Math

Co-ordinate Geometry

Hyperbola

Tangents are drawn to the hyperbola $9x_{2} −4y_{2} =1$ parallet to the sraight line $2x−y=1.$ The points of contact of the tangents on the hyperbola are (A) $(22 2 ,2 1 )$ (B) $(−22 9 ,2 1 )$ (C) $(33 ,−22 )$ (D) $(−33 ,22 )$

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Statement 1 : If (3, 4) is a point on a hyperbola having foci (3, 0) and $(λ,0)$ , the length of the transverse axis being 1 unit, then $λ$ can take the value 0 or 3. Statement 2 : $∣∣ S_{prime}P−SP∣∣ =2a,$ where $SandS_{′}$ are the two foci, $2a$ is the length of the transverse axis, and $P$ is any point on the hyperbola.

Find the equation of the hyperbola which has $3x−4y+7=0$ and $4x+3y+1=0$ as its asymptotes and which passes through the origin.

If the vertex of a hyperbola bisects the distance between its center and the correspoinding focus, then the ratio of the square of its conjugate axis to the square of its transverse axis is 2 (b) 4 (c) 6 (d) 3

The distance between two directrices of a rectangular hyperbola is 10 units. Find the distance between its foci.

If the distance between two parallel tangents having slope $m$ drawn to the hyperbola $9x_{2} −49y_{2} =1$ is 2, then the value of $2∣m∣$ is_____

The chord $PQ$ of the rectangular hyperbola $xy=a_{2}$ meets the axis of $x$ at $A;C$ is the midpoint of $PQ;$ and $O$ is the origin. Then $ΔACO$ is equilateral (b) isosceles right-angled (d) right isosceles

Let $aandb$ be nonzero real numbers. Then the equation $(ax_{2}+by_{2}+c)(x_{2}−5xy+6y_{2})=0$ represents. four straight lines, when $c=0$ and $a,b$ are of the same sign. two straight lines and a circle, when $a=b$ and $c$ is of sign opposite to that $a$ two straight lines and a hyperbola, when $aandb$ are of the same sign and $c$ is of sign opposite to that of $a$ a circle and an ellipse, when $aandb$ are of the same sign and $c$ is of sign opposite to that of $a$

Find the equation of hyperbola : Whose foci are (4, 2) and (8, 2) and accentricity is 2.