Q.
List I
List II
P
If the distance between two parallel tangents having slope $m$ drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{49}=1$ is 2 , then $\frac{2}{5}| m |$ is equal to
1
5
Q
If a variable line has its intercepts on the coordinate axes e and e', where $\frac{ e }{2}$ and $\frac{ e ^{\prime}}{2}$ are the eccentricities of a hyperbola and its conjugate hyperbola, then the line always touches the circle $x^2+y^2=r^2$, where $r$ is equal to
2
4
R
If the equation of line touching both parabolas $y^2-4 x=0$ and $x ^2+32 y =0$ is $ax -2 y + b =0( a , b \in R )$, then $( a + b )$ is equal to
3
2
S
If the mid-point of a chord of the ellipse $\frac{x^2}{16}+\frac{y^2}{25}=1$ is $M(0,3)$ and the length of chord is $\frac{8 p }{5}$, then $p$ is equal to
4
1
| List I | List II | ||
|---|---|---|---|
| P | If the distance between two parallel tangents having slope $m$ drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{49}=1$ is 2 , then $\frac{2}{5}| m |$ is equal to | 1 | 5 |
| Q | If a variable line has its intercepts on the coordinate axes e and e', where $\frac{ e }{2}$ and $\frac{ e ^{\prime}}{2}$ are the eccentricities of a hyperbola and its conjugate hyperbola, then the line always touches the circle $x^2+y^2=r^2$, where $r$ is equal to | 2 | 4 |
| R | If the equation of line touching both parabolas $y^2-4 x=0$ and $x ^2+32 y =0$ is $ax -2 y + b =0( a , b \in R )$, then $( a + b )$ is equal to | 3 | 2 |
| S | If the mid-point of a chord of the ellipse $\frac{x^2}{16}+\frac{y^2}{25}=1$ is $M(0,3)$ and the length of chord is $\frac{8 p }{5}$, then $p$ is equal to | 4 | 1 |
Conic Sections
Solution: