Question

For the ellipse $4x^2+5y^2=20$, observe the following lists:

List I	List II
A. Equation of auxiliary circle	1. $4x+5y=20$
B. Equation of director circle	2. $x^2+y^2=5$
C. Equation of tangent at $(1,1)$	3. $y-x+9=0$
D. Equation of tangent with slope $1$	4. $x^2+y^2=9$
	5. $5x+4y=20$
	6. $y=x+3$

The correct match for List I from List II is

• A. A - 2, B - 4, C - 1, D - 6
• B. A - 4, B - 2, C - 6, D - 5
• C. A - 4, B - 3, C - 1, D - 6
• D. A - 4, B - 2, C - 1, D - 3

Answer 1

The correct option is A A - 2, B - 4, C - 1, D - 6

$4x^2+5y^2=20$

$\Rightarrow \frac{x^2}{5}+\frac{y^2}{4}=1$

A] Equation of auxiliary circle : $x^2+y^2=a^2$

$x^2+y^2=5$

B] Equation of director circle: $x^2+y^2=a^2+b^2$

$x^2+y^2=9$

C] Equation of tangent at $(1,1):\frac{x}{a^2}+\frac{y}{b^2}=1$

$4x+5y=20$

D] Equation of tangent with slope 1 $:y=x\pm \sqrt{a^2+b^2}$

$y=x\pm 3$

$\therefore$ Option[A] A-1,B-4,C-1,D-6