If 3x+4y=12√2 is a tangent to the ellipse (x2/a2)+(y2/9)=1 for some a ∈ R, then the distance between the foci of the ellipse is :

Question

If 3x+4y=12√2 is a tangent to the ellipse (x2/a2)+(y2/9)=1 for some a ∈ R, then the distance between the foci of the ellipse is : (A) 2√5 (B) 2√7 (C) 2√2 (D) 4

Tardigrade Admin · Accepted Answer

3x+4y=12√12 is tangent to (x2/a2)+(y2/9)=1 c2=m2a2+b2 ⇒ a2=16 e=√1-(9/16)=(√7/4) Distance between focii = 2ae =2√7

Q. If $3 x + 4 y = 122$ is a tangent to the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{9} = 1$ for some $a \in R,$ then the distance between the foci of the ellipse is :

$25$

$27$

$22$

$4$

$3 x + 4 y = 1212$ is tangent to $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{9} = 1$
$c^{2} = m^{2} a^{2} + b^{2}$
$\Rightarrow a^{2} = 16$
$e = 1 - \frac{9}{16} = \frac{7}{4}$
Distance between focii $= 2 a e = 27$

Q. If 3x+4y=122​ is a tangent to the ellipse a2x2​+9y2​=1 for some a∈R, then the distance between the foci of the ellipse is :

25​

27​

22​

4

3x+4y=1212​ is tangent to a2x2​+9y2​=1 c2=m2a2+b2 ⇒a2=16 e=1−169​​=47​​ Distance between focii =2ae=27​

Q. If $3 x + 4 y = 122$ is a tangent to the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{9} = 1$ for some $a \in R,$ then the distance between the foci of the ellipse is :

$25$

$27$

$22$

$4$

$3 x + 4 y = 1212$ is tangent to $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{9} = 1$
$c^{2} = m^{2} a^{2} + b^{2}$
$\Rightarrow a^{2} = 16$
$e = 1 - \frac{9}{16} = \frac{7}{4}$
Distance between focii $= 2 a e = 27$