If the equation of translated parabola is $y^{2} + 25 = 4 x + 6 y$ , then what will be the coordinates of point to which the parabola $y^{2} = 4 x$ is translated?

(4, - 3)

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

(2, - 3)

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

(4, 3)

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

(3, 4)

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

Open in App

Solution

The correct option is C $(4, 3)$
Given, the equation of translated parabola as $y^{2} + 25 = 4 x + 6 y .$
On re-arranging and manipulating we get,
$\Rightarrow y^{2} - 6 y + 25 = 4 x$
$\Rightarrow y^{2} - (2 \times 3 \times y) + 9 + 16 = 4 x$
$\Rightarrow (y - 3)^{2} = 4 x - 16$
$\Rightarrow (y - 3)^{2} = 4 (x - 4)$
Now, on comparing with general equation of translated parabola $(y - k)^{2} = 4 a (x - h)$ we get $k = 3, h = 4,$ and $a = 1.$
From here we can also conclude that the old parabola equation must be $y^{2} = 4 x .$
So, the coordinates of point to which the parabola $y^{2} = 4 x$ is shifted is $(h, k)$ i.e $(4, 3) .$

Suggest Corrections

Similar questions

y^{2} = 4 x

(0, - 2)

y^{2} = 16 x

(1, 4) .

y^{2} + a x + b y + c = 0.

(a + b + c)

y^{2} - 2 y + 17 = 8 x

x = y^{2} + 2 y + 5 ?

P (5, 5)

x^{2} + y^{2} - 4 x - 6 y - 12 = 0

x^{2} + y^{2} = 25

P =

Join BYJU'S Learning Program