Class 12

Math

Co-ordinate Geometry

Hyperbola

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

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

Tangents are drawn from the points on a tangent of the hyperbola $x_{2}−y_{2}=a_{2}$ to the parabola $y_{2}=4ax˙$ If all the chords of contact pass through a fixed point $Q,$ prove that the locus of the point $Q$ for different tangents on the hyperbola is an ellipse.

Let $P$ be a point on the hyperbola $x_{2}−y_{2}=a_{2},$ where $a$ is a parameter, such that $P$ is nearest to the line $y=2x˙$ Find the locus of $P˙$

If values of a, for which the line $y=ax+25 $ touches the hyperbola $16x_{2}−9y_{2}=144$ are the roots of the equation $x_{2}−(a_{1}+b_{1})x−4=0$, then the values of $a_{1}+b_{1}$ is

On which curve does the perpendicular tangents drawn to the hyperbola $25x_{2} −16y_{2} =1$ intersect?

For hyperbola whose center is at (1, 2) and the asymptotes are parallel to lines $2x+3y=0$ and $x+2y=1$ , the equation of the hyperbola passing through (2, 4) is $(2x+3y−5)(x+2y−8)=40$ $(2x+3y−8)(x+2y−8)=40$ $(2x+3y−8)(x+2y−5)=30$ none of these

The equation of the transvers and conjugate axes of a hyperbola are, respectively, $x+2y−3=0$ and $2x−y+4=0$ , and their respective lengths are $2 $ and $23 ˙$ The equation of the hyperbola is $52 (x+2y−3)_{2}−53 (2x−y+4)_{2}=1$ $52 (x−y−4)_{2}−53 (x+2y−3)_{2}=1$ $2(2x−y+4)_{2}−3(x+2y−3)_{2}=1$ $2(x+2y−3)_{2}−3(2x−y+4)_{2}=1$

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.