First slide

Parabola

Question

$The vertex of the parabola 2 ((x - 1)^{2} + (y - 2)^{2}) = (x + y + 3) i s$

Moderate

A

$(- \frac{1}{2}, - \frac{1}{2})$
B

$(- \frac{1}{2}, \frac{1}{2})$
C

$(\frac{1}{2}, \frac{1}{2})$
D

$(\frac{1}{2}, - \frac{1}{2})$

Solution

$\begin{aligned} 2 ((x - 1)^{2} + (y - 2)^{2}) = (x + y + 3)^{2} \\ \Rightarrow \sqrt{(x - 1)^{2} + (y - 2)^{2}} = \frac{| x + y + 3 |}{\sqrt{2}} \end{aligned}$
$So, focus is S (1, 2) and directrix is x + y + 3 = 0 .$
$Axis of the parabola is x - y + 1 = 0$
$Solving directrix and axis, we get foot of perpendicular of$ $directrix on axis as A (- 2, - 1) .$
$Therefore, vertex is mid-point of A S which is (- \frac{1}{2}, \frac{1}{2}) .$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App