Class 11

Math

Co-ordinate Geometry

Hyperbola

If a hyperbola passing through the origin has $3x−4y−1=0$ and $4x−3y−6=0$ as its asymptotes, then find the equation of its transvers and conjugate axes.

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Two straight lines pass through the fixed points $(±a,0)$ and have slopes whose products is $p>0$ Show that the locus of the points of intersection of the lines is a hyperbola.

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_____

Tangents are drawn from any point on the hyperbola $9x_{2} −4y_{2} =1$ to the circle $x_{2}+y_{2}=9$ . Find the locus of the midpoint of the chord of contact.

The combined equation of the asymptotes of the hyperbola $2x_{2}+5xy+2y_{2}+4x+5y=0$ is $2x_{2}+5xy+2y_{2}+4x+5y+2=0$ $2x_{2}+5xy+2y_{2}+4x+5y−2=0$ $2x_{2}+5xy+2y_{2}=0$ none of these

Find the equation of the asymptotes of the hyperbola $3x_{2}+10xy+9y_{2}+14x+22y+7=0$

Tangents are drawn to the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ at two points whose eccentric angles are $α−β$ and $α+β$ The coordinates of their point of intersection are

Find the vertices of the hyperbola $9x_{2}−16y_{2}−36x+96y−252=0$

$PQ$ 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 $CS˙$