Find the equation of the parabola whose latus rectum is $4$ units, axis is the line $3 x + 4 y = 4$ and the tangent at the vertex is the line $4 x - 3 y + 7 = 0$ .

(3 x + 4 y - 4)^{2} = 4 (4 x - 3 y + 7)

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(3 x + 4 y + 4)^{2} = 4 (4 x - 3 y + 7)

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(3 x + 4 y + 4)^{2} = 4 (4 x - 3 y - 7)

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

(3 x + 4 y - 4)^{2} = 4 (4 x - 3 y - 7)

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Solution

The correct option is A $(3 x + 4 y - 4)^{2} = 4 (4 x - 3 y + 7)$
Given latus rectum of the parabola is, $4 a = 4 \Rightarrow a = 1$

also axis is $Y = 3 x + 4 y - 4 = 0$ and tangent at the vertex is $X = 4 x - 3 y + 7 = 0$

So the required parabola is $Y^{2} = 4 a X$

$\Rightarrow (3 x + 4 y - 4)^{2} = 4 (4 x - 3 y + 7)$

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Find the equation of the parabola whose latus rectum is 4 units, axis is the line 3x+4y=4 and the tangent at the vertex is the line 4x−3y+7=0.

The correct option is A (3x+4y−4)2=4(4x−3y+7)Given latus rectum of the parabola is, 4a=4⇒a=1also axis is Y=3x+4y−4=0 and tangent at the vertex is X=4x−3y+7=0So the required parabola is Y2=4aX⇒(3x+4y−4)2=4(4x−3y+7)

Find the equation of the parabola whose latus rectum is $4$ units, axis is the line $3 x + 4 y = 4$ and the tangent at the vertex is the line $4 x - 3 y + 7 = 0$ .