If e_1 and e_2 are the eccentricities of the ellipse (x^2)/18+(y^2)/4=1 and the hyperbola (x^2)/9-(y^2)/4=1 respectively and e_1,e_2 is a point on the…

Question

If e_1 and e_2 are the eccentricities of the ellipse (x^2)/18+(y^2)/4=1 and the hyperbola (x^2)/9-(y^2)/4=1 respectively and e_1,e_2 is a point on the ellipse 15x^2+3y^2=k , then the value of k is equal to

MARKS Content Team · Accepted Answer

Correct answer: (A) 16. e_1=√(1-418)=√79=(√7)/3 e_1=√(1+49)=√139=(√13)/3 Also, 15e12+3e22=k⇒k=157/9+313/9 ∴k=16

If $e_{1}$ and $e_{2}$ are the eccentricities of the ellipse $\frac{x^{2}}{18} + \frac{y^{2}}{4} = 1$ and the hyperbola $\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1$ respectively and $(e_{1}, e_{2})$ is a point on the ellipse $15 x^{2} + 3 y^{2} = k$ , then the value of $k$ is equal to

Solution

More Hyperbola Questions

If e1 and e2 are the eccentricities of the ellipse x218+y24=1 and the hyperbola x29-y24=1 respectively and e1,e2 is a point on the ellipse 15x2+3y2=k , then the value of k is equal to

Solution

More Hyperbola Questions

If $e_{1}$ and $e_{2}$ are the eccentricities of the ellipse $\frac{x^{2}}{18} + \frac{y^{2}}{4} = 1$ and the hyperbola $\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1$ respectively and $(e_{1}, e_{2})$ is a point on the ellipse $15 x^{2} + 3 y^{2} = k$ , then the value of $k$ is equal to