You visited us 1 times! Enjoying our articles? Unlock Full Access!

Idea of a Set

Let eccentric...

Question

Let eccentricity of ellipse with focii $z_{1}$ and $z_{2}$ be $1 / 3$ . If $| z_{1} - z_{2} | = 5$ and $z$ lies on the ellipse, find maximum possible value of $| z - z_{1} |$ .

Open in App

Solution

From the figure:
$| z_{1} - z_{2} | = 2 a e = 5$
$\Rightarrow a = \frac{15}{2}$
now, $m a x (| z - z_{1} |) = a + a e = \frac{15}{2} (1 + \frac{1}{3}) = 10$
Ans: 10

Suggest Corrections

Similar questions

A (z_{1}) and B (z_{2})

e

e

If $| z - z_{1} | + | z + z_{2} |$ = $λ, λ \in R^{+}, z_{1}, z_{2}$ are fixed complex numbers, represents an ellipse, then:

z_{1}

z_{2}

| z_{1} | = | z_{2} | + | z_{1} - z_{2} |

(\frac{z_{1}}{z_{2}}) = 0

\Rightarrow z

z_{1}

z_{2}

z = (1 - t) z_{1} + t z_{2}

t

0 < t < 1

(ω)

ω

z_{2} = {\bar{z}}_{1}

z_{2} = \frac{1}{z_{1}}

Join BYJU'S Learning Program