Mathematics - Ellipse Question with Solution | TestHub

MathematicsEllipseGeneralMedium2 minQB

MathematicsMediuminteger

The distance between the directrices of the ellipse $(4 x - 8)^{2} + 16 y^{2} = (x + 3 y + 10)^{2}$ is $K$ then $\frac{K}{2}$ is

Answer:

Solution:

$(x - 2)^{2} + y^{2} = (\frac{1}{2})^{2} \frac{( x + 3 y + 10 ) ^{2}}{4}$

$(h, k) = (z, 0), e = 1/2$

Perpendicular distance from $(2, 0)$ to $x + 3 y + 10 = 0$ is $\frac{a}{e} - a e$

$2 a - \frac{a}{2} = 6 \Rightarrow a = 4$

Distance between directrics $= \frac{2 a}{e} = 16 = K$

Stream:JEESubject:MathematicsTopic:EllipseSubtopic:General

⏱ 2mℹ️ Source: QB

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