lf the equation $25 [(x - 5)^{2} + (y - 3)^{2}] = (3 x - 4 y + 1)^{2}$ represents a parabola then its axis is

4 x + 3 y - 10 = 0

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4 x + 3 y - 15 = 0

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4 x + 3 y - 29 = 0

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4 x + 3 y - 17 = 0

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Solution

The correct option is A $4 x + 3 y - 29 = 0$
Given parabola may be written as,
$(x - 5)^{2} + (y - 3)^{2} = {∣ ∣ ∣ ∣ \frac{3 x - 4 y + 1}{\sqrt{3^{2} + 4^{2}}} ∣ ∣ ∣ ∣}^{2}$
Thus the focus of the parabola is $(5, 3)$ and directrix is, $3 x - 4 y + 1 = 0$
Therefore the equation of axis of the parabola will perpendicular to the directrix and is given by,
$4 x + 3 y + k = 0$ ,
Also axis passes through focus, $\Rightarrow 4.5 + 3.3 + k = 0 \Rightarrow k = - 29$
Hence required line is $4 x + 3 y - 29 = 0$

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lf the equation 25[(x−5)2+(y−3)2]=(3x−4y+1)2 represents a parabola then its axis is

lf the equation $25 [(x - 5)^{2} + (y - 3)^{2}] = (3 x - 4 y + 1)^{2}$ represents a parabola then its axis is