The length of the latus rectum of the parabola $169 [(x - 1)^{2} + (y - 3)^{2}] = (5 x - 12 y + 17)^{2}$ is:

\frac{14}{13}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{12}{13}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{28}{13}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

n o n e o f t h e s e

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $\frac{28}{13}$
Given equation can be rewritten as
${(x - 1)}^{2} + {(y - 3)}^{2} = {(\frac{5 x - 12 y + 17}{13})}^{2}$
$\Rightarrow S P = P M$
Here, focus is $(1, 3)$ , directrix
$5 x - 12 y + 17 = 0$
$∴$ the distance of the focus from the directrix
$= ∣ ∣ ∣ \frac{5 - 36 + 17}{\sqrt{25 + 144}} ∣ ∣ ∣$
$= \frac{14}{13} = 2 a$
$∴$ Latusrectum $= 2 \times \frac{14}{13} = \frac{28}{13}$

Suggest Corrections

Similar questions

169 {(x - 1)^{2} + (y - 3)^{2}} = (5 x - 12 y + 17)^{2}

169 {(x - 1)^{2} + (y - 3)^{2}} = (5 x - 12 y + 17)^{2}

169 {(x - 1)^{2} + (y - 3)^{2}} = (5 x - 12 y + 17)^{2}

(a) If the equation $λ x^{2} 4 x y + y^{2} + λ x + 3 y + 2 = 0$ represents a parabola then find

(b) Find the length of latus rectum of the parabola $169 {(x - 1)^{2} + {(y - 3)}^{2}} = (5 x - 12 y + 17)^{2} .$

169 {{(x - 1)}^{2} + {(y - 3)}^{2}} = {(5 x - 12 y + 17)}^{2}

Join BYJU'S Learning Program