Q.
Column I
Column II
A
The minimum and maximum distance of a point $(2,6)$ from the ellipse are $9 x^2+8 y^2-36 x-16 y-28=0$
p
0
B
The minimum and maximum distance of a point $\left(\frac{9}{5}, \frac{12}{5}\right)$ from the ellipse $4(3 x+4 y)^2+9(4 x-3 y)^2=900$ are
q
2
C
If $E: 2 x^2+y^2=2$ and director circle of $E$ is $C_1$, director circle of $C _1$ is $C _2$ director circle of $C _2$ is $C _3$ and so on. If $r _1, r _2, r _3 \ldots$ are the radii of $C _1, C _2, C _3 \ldots$ respectively then G.M. of $r_1^2, r_2^2, r_3^2$ is
r
6
D
Minimum area of the triangle formed by any tangent to the ellipse $x^2+4 y^2=16$ with coordinate axes is
s
8
| Column I | Column II | ||
|---|---|---|---|
| A | The minimum and maximum distance of a point $(2,6)$ from the ellipse are $9 x^2+8 y^2-36 x-16 y-28=0$ | p | 0 |
| B | The minimum and maximum distance of a point $\left(\frac{9}{5}, \frac{12}{5}\right)$ from the ellipse $4(3 x+4 y)^2+9(4 x-3 y)^2=900$ are | q | 2 |
| C | If $E: 2 x^2+y^2=2$ and director circle of $E$ is $C_1$, director circle of $C _1$ is $C _2$ director circle of $C _2$ is $C _3$ and so on. If $r _1, r _2, r _3 \ldots$ are the radii of $C _1, C _2, C _3 \ldots$ respectively then G.M. of $r_1^2, r_2^2, r_3^2$ is | r | 6 |
| D | Minimum area of the triangle formed by any tangent to the ellipse $x^2+4 y^2=16$ with coordinate axes is | s | 8 |
Conic Sections
Solution:
